90=(4w-9)(w)

Solution for 90=(4w-9)(w) equation:

90=(4w-9)(w)

We move all terms to the left:

90-((4w-9)(w))=0


We calculate terms in parentheses: -((4w-9)w), so:

(4w-9)w

We multiply parentheses

4w^2-9w

Back to the equation:

-(4w^2-9w)


We get rid of parentheses

-4w^2+9w+90=0

a = -4; b = 9; c = +90;
Δ = b2-4ac
Δ = 92-4·(-4)·90
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-39}{2*-4}=\frac{-48}{-8}
=+6
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+39}{2*-4}=\frac{30}{-8}
=-3+3/4
$