7x^2+x=6x^2+13x-3

Solution for 7x^2+x=6x^2+13x-3 equation:

7x^2+x=6x^2+13x-3

We move all terms to the left:

7x^2+x-(6x^2+13x-3)=0

We get rid of parentheses

7x^2-6x^2+x-13x+3=0

We add all the numbers together, and all the variables

x^2-12x+3=0

a = 1; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·1·3
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{33}}{2*1}=\frac{12-2\sqrt{33}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{33}}{2*1}=\frac{12+2\sqrt{33}}{2}
$