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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2-1x+19=0

a = -2; b = -1; c = +19;
Δ = b2-4ac
Δ = -12-4·(-2)·19
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3\sqrt{17}}{2*-2}=\frac{1-3\sqrt{17}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3\sqrt{17}}{2*-2}=\frac{1+3\sqrt{17}}{-4}
$