80=x(x+10)+66

Solution for 80=x(x+10)+66 equation:

80=x(x+10)+66

We move all terms to the left:

80-(x(x+10)+66)=0


We calculate terms in parentheses: -(x(x+10)+66), so:

x(x+10)+66

We multiply parentheses

x^2+10x+66

Back to the equation:

-(x^2+10x+66)


We get rid of parentheses

-x^2-10x-66+80=0

We add all the numbers together, and all the variables

-1x^2-10x+14=0

a = -1; b = -10; c = +14;
Δ = b2-4ac
Δ = -102-4·(-1)·14
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{39}}{2*-1}=\frac{10-2\sqrt{39}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{39}}{2*-1}=\frac{10+2\sqrt{39}}{-2}
$