1=8x2+7x-1

Solution for 1=8x2+7x-1 equation:

1=8x^2+7x-1

We move all terms to the left:

1-(8x^2+7x-1)=0

We get rid of parentheses

-8x^2-7x+1+1=0

We add all the numbers together, and all the variables

-8x^2-7x+2=0

a = -8; b = -7; c = +2;
Δ = b2-4ac
Δ = -72-4·(-8)·2
Δ = 113
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{-(-7)-\sqrt{113}}{2*-8}=\frac{7-\sqrt{113}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{113}}{2*-8}=\frac{7+\sqrt{113}}{-16}
$