(3w-7)w=35

Solution for (3w-7)w=35 equation:

(3w-7)w=35

We move all terms to the left:

(3w-7)w-(35)=0

We multiply parentheses

3w^2-7w-35=0

a = 3; b = -7; c = -35;
Δ = b2-4ac
Δ = -72-4·3·(-35)
Δ = 469
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{469}}{2*3}=\frac{7-\sqrt{469}}{6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{469}}{2*3}=\frac{7+\sqrt{469}}{6}
$