0=10x^2+22x-66

Solution for 0=10x^2+22x-66 equation:

0=10x^2+22x-66

We move all terms to the left:

0-(10x^2+22x-66)=0

We add all the numbers together, and all the variables

-(10x^2+22x-66)=0

We get rid of parentheses

-10x^2-22x+66=0

a = -10; b = -22; c = +66;
Δ = b2-4ac
Δ = -222-4·(-10)·66
Δ = 3124
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:

$\sqrt{\Delta}=\sqrt{3124}=\sqrt{4*781}=\sqrt{4}*\sqrt{781}=2\sqrt{781}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{781}}{2*-10}=\frac{22-2\sqrt{781}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{781}}{2*-10}=\frac{22+2\sqrt{781}}{-20}
$