(-8x)(-8x)+77x-89=0

Solution for (-8x)(-8x)+77x-89=0 equation:

(-8x)(-8x)+77x-89=0

We add all the numbers together, and all the variables

77x+(-8x)(-8x)-89=0

We multiply parentheses ..

(+64x^2)+77x-89=0

We get rid of parentheses

64x^2+77x-89=0

a = 64; b = 77; c = -89;
Δ = b2-4ac
Δ = 772-4·64·(-89)
Δ = 28713
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-\sqrt{28713}}{2*64}=\frac{-77-\sqrt{28713}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+\sqrt{28713}}{2*64}=\frac{-77+\sqrt{28713}}{128}
$