0=8x^2-17.5x-7.5

Solution for 0=8x^2-17.5x-7.5 equation:

0=8x^2-17.5x-7.5

We move all terms to the left:

0-(8x^2-17.5x-7.5)=0

We add all the numbers together, and all the variables

-(8x^2-17.5x-7.5)=0

We get rid of parentheses

-8x^2+17.5x+7.5=0

a = -8; b = 17.5; c = +7.5;
Δ = b2-4ac
Δ = 17.52-4·(-8)·7.5
Δ = 546.25
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{-(17.5)-\sqrt{546.25}}{2*-8}=\frac{-17.5-\sqrt{546.25}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17.5)+\sqrt{546.25}}{2*-8}=\frac{-17.5+\sqrt{546.25}}{-16}
$