-8w^2+18w-7=0

Solution for -8w^2+18w-7=0 equation:

-8w^2+18w-7=0

a = -8; b = 18; c = -7;
Δ = b2-4ac
Δ = 182-4·(-8)·(-7)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10}{2*-8}=\frac{-28}{-16}
=1+3/4
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10}{2*-8}=\frac{-8}{-16}
=1/2
$