w*(2w+3)=78

Solution for w*(2w+3)=78 equation:

w(2w+3)=78

We move all terms to the left:

w(2w+3)-(78)=0

We multiply parentheses

2w^2+3w-78=0

a = 2; b = 3; c = -78;
Δ = b2-4ac
Δ = 32-4·2·(-78)
Δ = 633
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{-(3)-\sqrt{633}}{2*2}=\frac{-3-\sqrt{633}}{4}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{633}}{2*2}=\frac{-3+\sqrt{633}}{4}
$