15=(2w-7)(w)

Solution for 15=(2w-7)(w) equation:

15=(2w-7)(w)

We move all terms to the left:

15-((2w-7)(w))=0


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

(2w-7)w

We multiply parentheses

2w^2-7w

Back to the equation:

-(2w^2-7w)


We get rid of parentheses

-2w^2+7w+15=0

a = -2; b = 7; c = +15;
Δ = b2-4ac
Δ = 72-4·(-2)·15
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-2}=\frac{-20}{-4}
=+5
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-2}=\frac{6}{-4}
=-1+1/2
$