8x^2+16x-75=0

Solution for 8x^2+16x-75=0 equation:

8x^2+16x-75=0

a = 8; b = 16; c = -75;
Δ = b2-4ac
Δ = 162-4·8·(-75)
Δ = 2656
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:

$\sqrt{\Delta}=\sqrt{2656}=\sqrt{16*166}=\sqrt{16}*\sqrt{166}=4\sqrt{166}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{166}}{2*8}=\frac{-16-4\sqrt{166}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{166}}{2*8}=\frac{-16+4\sqrt{166}}{16}
$