7x^2-7x=12x+36

Solution for 7x^2-7x=12x+36 equation:

7x^2-7x=12x+36

We move all terms to the left:

7x^2-7x-(12x+36)=0

We get rid of parentheses

7x^2-7x-12x-36=0

We add all the numbers together, and all the variables

7x^2-19x-36=0

a = 7; b = -19; c = -36;
Δ = b2-4ac
Δ = -192-4·7·(-36)
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-37}{2*7}=\frac{-18}{14}
=-1+2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+37}{2*7}=\frac{56}{14}
=4
$