(3w-11)w=70

Solution for (3w-11)w=70 equation:

(3w-11)w=70

We move all terms to the left:

(3w-11)w-(70)=0

We multiply parentheses

3w^2-11w-70=0

a = 3; b = -11; c = -70;
Δ = b2-4ac
Δ = -112-4·3·(-70)
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{-(-11)-31}{2*3}=\frac{-20}{6}
=-3+1/3
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*3}=\frac{42}{6}
=7
$