X^2+4x-58=18

Solution for X^2+4x-58=18 equation:

X^2+4X-58=18

We move all terms to the left:

X^2+4X-58-(18)=0

We add all the numbers together, and all the variables

X^2+4X-76=0

a = 1; b = 4; c = -76;
Δ = b2-4ac
Δ = 42-4·1·(-76)
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{5}}{2*1}=\frac{-4-8\sqrt{5}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{5}}{2*1}=\frac{-4+8\sqrt{5}}{2}
$