(-8.25x^2)+(66x)=8

Solution for (-8.25x^2)+(66x)=8 equation:

(-8.25x^2)+(66x)=8

We move all terms to the left:

(-8.25x^2)+(66x)-(8)=0

We get rid of parentheses

-8.25x^2+66x-8=0

a = -8.25; b = 66; c = -8;
Δ = b2-4ac
Δ = 662-4·(-8.25)·(-8)
Δ = 4092
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:

$\sqrt{\Delta}=\sqrt{4092}=\sqrt{4*1023}=\sqrt{4}*\sqrt{1023}=2\sqrt{1023}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-2\sqrt{1023}}{2*-8.25}=\frac{-66-2\sqrt{1023}}{-16.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+2\sqrt{1023}}{2*-8.25}=\frac{-66+2\sqrt{1023}}{-16.5}
$