2/z-5=0.5z2+7

Simple and best practice solution for 2/z-5=0.5z2+7 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so don`t hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

Solution for 2/z-5=0.5z2+7 equation:



2/z-5=0.5z^2+7
We move all terms to the left:
2/z-5-(0.5z^2+7)=0
Domain of the equation: z!=0
z∈R
We get rid of parentheses
-0.5z^2+2/z-7-5=0
We multiply all the terms by the denominator
-(0.5z^2)*z-7*z-5*z+2=0
We add all the numbers together, and all the variables
-12z-(0.5z^2)*z+2=0
We multiply parentheses
-0z^2-12z+2=0
We add all the numbers together, and all the variables
-1z^2-12z+2=0
a = -1; b = -12; c = +2;
Δ = b2-4ac
Δ = -122-4·(-1)·2
Δ = 152
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{38}}{2*-1}=\frac{12-2\sqrt{38}}{-2} $
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{38}}{2*-1}=\frac{12+2\sqrt{38}}{-2} $

See similar equations:

| 3x+8=2(5x-6) | | 42=x2+4x-150 | | 145x+150=135 | | 5y+2X2=12 | | 121x+179=36 | | 9x35+3x20-35=N | | 52x+2=66 | | 5.30x+7.5=55.20 | | Y2-4x=0 | | 3=4d | | r÷9=7 | | 6(2x+3)=14 | | 135x+168=93 | | 2x+10=2(35)+10=80 | | 2/3(x-6)=-8 | | 34x+29=33 | | X2+124x+49=1000 | | 42=x^2+4x-150 | | 4x-12+19=3x+12 | | 20-(3x+1)=2 | | (2x-1)2-4(3x+1=2 | | 30x+79=47 | | 5x-8=×+12 | | -5x+10+2x=-2 | | 62x+39=17 | | 8(4n+7)=152 | | 16x+50=24 | | -2=-5t+2t | | 94x+11=9 | | 56x+93=21 | | 4m-8=3m+1 | | 3y–5=12 |

Equations solver categories