2x=x2+7x-22

Solution for 2x=x2+7x-22 equation:

2x=x2+7x-22

We move all terms to the left:

2x-(x2+7x-22)=0

We add all the numbers together, and all the variables

-(+x^2+7x-22)+2x=0

We get rid of parentheses

-x^2-7x+2x+22=0

We add all the numbers together, and all the variables

-1x^2-5x+22=0

a = -1; b = -5; c = +22;
Δ = b2-4ac
Δ = -52-4·(-1)·22
Δ = 113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{113}}{2*-1}=\frac{5-\sqrt{113}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{113}}{2*-1}=\frac{5+\sqrt{113}}{-2}
$