2x^2-24x=-22

Solution for 2x^2-24x=-22 equation:

2x^2-24x=-22

We move all terms to the left:

2x^2-24x-(-22)=0

We add all the numbers together, and all the variables

2x^2-24x+22=0

a = 2; b = -24; c = +22;
Δ = b2-4ac
Δ = -242-4·2·22
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-20}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+20}{2*2}=\frac{44}{4}
=11
$