X^2-76=-6x

Solution for X^2-76=-6x equation:

X^2-76=-6X

We move all terms to the left:

X^2-76-(-6X)=0

We get rid of parentheses

X^2+6X-76=0

a = 1; b = 6; c = -76;
Δ = b2-4ac
Δ = 62-4·1·(-76)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{85}}{2*1}=\frac{-6-2\sqrt{85}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{85}}{2*1}=\frac{-6+2\sqrt{85}}{2}
$