13-6x=4x^2-22

Solution for 13-6x=4x^2-22 equation:

13-6x=4x^2-22

We move all terms to the left:

13-6x-(4x^2-22)=0

We get rid of parentheses

-4x^2-6x+22+13=0

We add all the numbers together, and all the variables

-4x^2-6x+35=0

a = -4; b = -6; c = +35;
Δ = b2-4ac
Δ = -62-4·(-4)·35
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{149}}{2*-4}=\frac{6-2\sqrt{149}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{149}}{2*-4}=\frac{6+2\sqrt{149}}{-8}
$