F(z)=2z-8/7z+2

Simple and best practice solution for F(z)=2z-8/7z+2 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 F(z)=2z-8/7z+2 equation:



(F)=2F-8/7F+2
We move all terms to the left:
(F)-(2F-8/7F+2)=0
Domain of the equation: 7F+2)!=0
F∈R
We get rid of parentheses
F-2F+8/7F-2=0
We multiply all the terms by the denominator
F*7F-2F*7F-2*7F+8=0
Wy multiply elements
7F^2-14F^2-14F+8=0
We add all the numbers together, and all the variables
-7F^2-14F+8=0
a = -7; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·(-7)·8
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{105}}{2*-7}=\frac{14-2\sqrt{105}}{-14} $
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{105}}{2*-7}=\frac{14+2\sqrt{105}}{-14} $

See similar equations:

| x^2-12x+67=0 | | 0.3=0.5^x | | 3x-3+22=4x-1+9x | | 3.6=1.2r | | -3(k-1)=3(k+1)-48 | | 4x-2(2-3x)=4(x-4)-6 | | 8y-4×=12 | | 4(k-4)-3(k+1)-14=-26 | | X+x+6=20-x | | x^2+10x-24=-9 | | 3x-3+22=5x-1+8x | | 25-3x=5+x | | 12P=3b^2 | | -5(3w+1)-w=43 | | 0=28x-3x^2 | | n+7/9=17/18 | | 9k×96=98;K= | | -500x(2x-9)=0 | | 4x=9x-2 | | 1/x+1/7=3/7 | | 2x+18=19+x | | k-7/8=3/8 | | 180=x+x+2x | | 6h=7=3(4h-71)-8 | | X-2(143-x)=37 | | 6(3-2x)-12=-4(5x-4) | | 180=7x+3x+90 | | 6(3-2x)-12=4(5x-4) | | 4.9t^2+1.55t-2.2=0 | | 30=-3x-6(-5x+40) | | -2v^2+4v+45=0 | | 28p+8=64 |

Equations solver categories