-8w2+14w-3=0

Solution for -8w2+14w-3=0 equation:

-8w^2+14w-3=0

a = -8; b = 14; c = -3;
Δ = b2-4ac
Δ = 142-4·(-8)·(-3)
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{-(14)-10}{2*-8}=\frac{-24}{-16}
=1+1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+10}{2*-8}=\frac{-4}{-16}
=1/4
$