0=8x^2+x-5

Solution for 0=8x^2+x-5 equation:

0=8x^2+x-5

We move all terms to the left:

0-(8x^2+x-5)=0

We add all the numbers together, and all the variables

-(8x^2+x-5)=0

We get rid of parentheses

-8x^2-x+5=0

We add all the numbers together, and all the variables

-8x^2-1x+5=0

a = -8; b = -1; c = +5;
Δ = b2-4ac
Δ = -12-4·(-8)·5
Δ = 161
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{-(-1)-\sqrt{161}}{2*-8}=\frac{1-\sqrt{161}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{161}}{2*-8}=\frac{1+\sqrt{161}}{-16}
$