w(3w-5)=78

Solution for w(3w-5)=78 equation:

w(3w-5)=78

We move all terms to the left:

w(3w-5)-(78)=0

We multiply parentheses

3w^2-5w-78=0

a = 3; b = -5; c = -78;
Δ = b2-4ac
Δ = -52-4·3·(-78)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-31}{2*3}=\frac{-26}{6}
=-4+1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+31}{2*3}=\frac{36}{6}
=6
$