x^2-30=6x+50

Solution for x^2-30=6x+50 equation:

x^2-30=6x+50

We move all terms to the left:

x^2-30-(6x+50)=0

We get rid of parentheses

x^2-6x-50-30=0

We add all the numbers together, and all the variables

x^2-6x-80=0

a = 1; b = -6; c = -80;
Δ = b2-4ac
Δ = -62-4·1·(-80)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{89}}{2*1}=\frac{6-2\sqrt{89}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{89}}{2*1}=\frac{6+2\sqrt{89}}{2}
$