6x^2-35x=12x^2+13x

Solution for 6x^2-35x=12x^2+13x equation:

6x^2-35x=12x^2+13x

We move all terms to the left:

6x^2-35x-(12x^2+13x)=0

We get rid of parentheses

6x^2-12x^2-35x-13x=0

We add all the numbers together, and all the variables

-6x^2-48x=0

a = -6; b = -48; c = 0;
Δ = b2-4ac
Δ = -482-4·(-6)·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-48}{2*-6}=\frac{0}{-12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+48}{2*-6}=\frac{96}{-12}
=-8
$