8+(8x-9)(10x+7)=0

Solution for 8+(8x-9)(10x+7)=0 equation:

8+(8x-9)(10x+7)=0

We multiply parentheses ..

(+80x^2+56x-90x-63)+8=0

We get rid of parentheses

80x^2+56x-90x-63+8=0

We add all the numbers together, and all the variables

80x^2-34x-55=0

a = 80; b = -34; c = -55;
Δ = b2-4ac
Δ = -342-4·80·(-55)
Δ = 18756
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:

$\sqrt{\Delta}=\sqrt{18756}=\sqrt{36*521}=\sqrt{36}*\sqrt{521}=6\sqrt{521}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-6\sqrt{521}}{2*80}=\frac{34-6\sqrt{521}}{160}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+6\sqrt{521}}{2*80}=\frac{34+6\sqrt{521}}{160}
$