144=(2w+7)(w)

Solution for 144=(2w+7)(w) equation:

144=(2w+7)(w)

We move all terms to the left:

144-((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+144=0

a = -2; b = -7; c = +144;
Δ = b2-4ac
Δ = -72-4·(-2)·144
Δ = 1201
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{1201}}{2*-2}=\frac{7-\sqrt{1201}}{-4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1201}}{2*-2}=\frac{7+\sqrt{1201}}{-4}
$