1/2x+10=x-2

Simple and best practice solution for 1/2x+10=x-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 1/2x+10=x-2 equation:



1/2x+10=x-2
We move all terms to the left:
1/2x+10-(x-2)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We get rid of parentheses
1/2x-x+2+10=0
We multiply all the terms by the denominator
-x*2x+2*2x+10*2x+1=0
Wy multiply elements
-2x^2+4x+20x+1=0
We add all the numbers together, and all the variables
-2x^2+24x+1=0
a = -2; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·(-2)·1
Δ = 584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{584}=\sqrt{4*146}=\sqrt{4}*\sqrt{146}=2\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{146}}{2*-2}=\frac{-24-2\sqrt{146}}{-4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{146}}{2*-2}=\frac{-24+2\sqrt{146}}{-4} $

See similar equations:

| 34=2x+4 | | 18=7k | | 1/2x10=x-2 | | 4/7k-9/5=3-9/5k | | 16q^2-16q+4=0 | | 2(3x+6)=8x-8 | | 10n+32=2n | | 3×(x-5)=30 | | 3n+2=n+1+2n+2 | | -3x+6=-3x-9 | | 42-6x+12=6 | | 3-(2x-1)=x+5+3x | | 5x-53x+20+x+60+4x-40=360 | | (4+4c)(2)= | | 8x+75=2x+114 | | 4-(-2x+13)=-8x+7 | | -4(2x+2)+5(3x-1=-20 | | 5(x-1)-5+3x+20+x+60+4(x-10)=360 | | 3(3+5j)= | | -12*x=-132 | | 0.25x+20=-1.75x+2 | | 129=5x-1 | | -1+3k=14 | | 2y-17=4 | | 2n+9=−17 | | 5/8×=3+1/2y | | 7+2(y-6)=28 | | 4j+9=45 | | 3y+(y+12)=180 | | x^2-12x+4=20 | | 0.5x+(x÷3)=0.25+7 | | u/11=-5 |

Equations solver categories