X^2+24x=-46

Solution for X^2+24x=-46 equation:

X^2+24X=-46

We move all terms to the left:

X^2+24X-(-46)=0

We add all the numbers together, and all the variables

X^2+24X+46=0

a = 1; b = 24; c = +46;
Δ = b2-4ac
Δ = 242-4·1·46
Δ = 392
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-14\sqrt{2}}{2*1}=\frac{-24-14\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+14\sqrt{2}}{2*1}=\frac{-24+14\sqrt{2}}{2}
$