8w^2+51w-35=0

Solution for 8w^2+51w-35=0 equation:

8w^2+51w-35=0

a = 8; b = 51; c = -35;
Δ = b2-4ac
Δ = 512-4·8·(-35)
Δ = 3721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3721}=61$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-61}{2*8}=\frac{-112}{16}
=-7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+61}{2*8}=\frac{10}{16}
=5/8
$