2x^2=-7x+22

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

2x^2=-7x+22

We move all terms to the left:

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

We get rid of parentheses

2x^2+7x-22=0

a = 2; b = 7; c = -22;
Δ = b2-4ac
Δ = 72-4·2·(-22)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-15}{2*2}=\frac{-22}{4}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+15}{2*2}=\frac{8}{4}
=2
$