2x^2=-23x-56

Solution for 2x^2=-23x-56 equation:

2x^2=-23x-56

We move all terms to the left:

2x^2-(-23x-56)=0

We get rid of parentheses

2x^2+23x+56=0

a = 2; b = 23; c = +56;
Δ = b2-4ac
Δ = 232-4·2·56
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-9}{2*2}=\frac{-32}{4}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+9}{2*2}=\frac{-14}{4}
=-3+1/2
$