X^2-20x+78=-4

Solution for X^2-20x+78=-4 equation:

X^2-20X+78=-4

We move all terms to the left:

X^2-20X+78-(-4)=0

We add all the numbers together, and all the variables

X^2-20X+82=0

a = 1; b = -20; c = +82;
Δ = b2-4ac
Δ = -202-4·1·82
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-6\sqrt{2}}{2*1}=\frac{20-6\sqrt{2}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+6\sqrt{2}}{2*1}=\frac{20+6\sqrt{2}}{2}
$