5=(7w+2)*w

Solution for 5=(7w+2)*w equation:

5=(7w+2)*w

We move all terms to the left:

5-((7w+2)*w)=0


We calculate terms in parentheses: -((7w+2)*w), so:

(7w+2)*w

We multiply parentheses

7w^2+2w

Back to the equation:

-(7w^2+2w)


We get rid of parentheses

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

a = -7; b = -2; c = +5;
Δ = b2-4ac
Δ = -22-4·(-7)·5
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-12}{2*-7}=\frac{-10}{-14}
=5/7
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+12}{2*-7}=\frac{14}{-14}
=-1
$