-8x^2+18x+1=0

Solution for -8x^2+18x+1=0 equation:

-8x^2+18x+1=0

a = -8; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·(-8)·1
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{89}}{2*-8}=\frac{-18-2\sqrt{89}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{89}}{2*-8}=\frac{-18+2\sqrt{89}}{-16}
$