0=8x^2-x-75

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

0=8x^2-x-75

We move all terms to the left:

0-(8x^2-x-75)=0

We add all the numbers together, and all the variables

-(8x^2-x-75)=0

We get rid of parentheses

-8x^2+x+75=0

a = -8; b = 1; c = +75;
Δ = b2-4ac
Δ = 12-4·(-8)·75
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-49}{2*-8}=\frac{-50}{-16}
=3+1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+49}{2*-8}=\frac{48}{-16}
=-3
$