5=7w+8w^2

Solution for 5=7w+8w^2 equation:

5=7w+8w^2

We move all terms to the left:

5-(7w+8w^2)=0

We get rid of parentheses

-8w^2-7w+5=0

a = -8; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·(-8)·5
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{209}}{2*-8}=\frac{7-\sqrt{209}}{-16}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{209}}{2*-8}=\frac{7+\sqrt{209}}{-16}
$