8x+8x^2-75=0

Solution for 8x+8x^2-75=0 equation:

8x+8x^2-75=0

a = 8; b = 8; c = -75;
Δ = b2-4ac
Δ = 82-4·8·(-75)
Δ = 2464
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:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{154}}{2*8}=\frac{-8-4\sqrt{154}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{154}}{2*8}=\frac{-8+4\sqrt{154}}{16}
$