5x+6=x^2-7+x^2-x

Solution for 5x+6=x^2-7+x^2-x equation:

5x+6=x^2-7+x^2-x

We move all terms to the left:

5x+6-(x^2-7+x^2-x)=0

We get rid of parentheses

-x^2-x^2+x+5x+7+6=0

We add all the numbers together, and all the variables

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

a = -2; b = 6; c = +13;
Δ = b2-4ac
Δ = 62-4·(-2)·13
Δ = 140
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:

$\sqrt{\Delta}=\sqrt{140}=\sqrt{4*35}=\sqrt{4}*\sqrt{35}=2\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{35}}{2*-2}=\frac{-6-2\sqrt{35}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{35}}{2*-2}=\frac{-6+2\sqrt{35}}{-4}
$