8x^2+10x=1

Solution for 8x^2+10x=1 equation:

8x^2+10x=1

We move all terms to the left:

8x^2+10x-(1)=0

a = 8; b = 10; c = -1;
Δ = b2-4ac
Δ = 102-4·8·(-1)
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{33}}{2*8}=\frac{-10-2\sqrt{33}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{33}}{2*8}=\frac{-10+2\sqrt{33}}{16}
$