x^2=156-10x

Solution for x^2=156-10x equation:

x^2=156-10x

We move all terms to the left:

x^2-(156-10x)=0

We add all the numbers together, and all the variables

x^2-(-10x+156)=0

We get rid of parentheses

x^2+10x-156=0

a = 1; b = 10; c = -156;
Δ = b2-4ac
Δ = 102-4·1·(-156)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{181}}{2*1}=\frac{-10-2\sqrt{181}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{181}}{2*1}=\frac{-10+2\sqrt{181}}{2}
$