X^2+23x=-126

Solution for X^2+23x=-126 equation:

X^2+23X=-126

We move all terms to the left:

X^2+23X-(-126)=0

We add all the numbers together, and all the variables

X^2+23X+126=0

a = 1; b = 23; c = +126;
Δ = b2-4ac
Δ = 232-4·1·126
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-5}{2*1}=\frac{-28}{2}
=-14
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+5}{2*1}=\frac{-18}{2}
=-9
$