100x^2-36=20x+12

Solution for 100x^2-36=20x+12 equation:

100x^2-36=20x+12

We move all terms to the left:

100x^2-36-(20x+12)=0

We get rid of parentheses

100x^2-20x-12-36=0

We add all the numbers together, and all the variables

100x^2-20x-48=0

a = 100; b = -20; c = -48;
Δ = b2-4ac
Δ = -202-4·100·(-48)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-140}{2*100}=\frac{-120}{200}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+140}{2*100}=\frac{160}{200}
=4/5
$