5(w-3)7w=-21

Solution for 5(w-3)7w=-21 equation:

5(w-3)7w=-21

We move all terms to the left:

5(w-3)7w-(-21)=0

We add all the numbers together, and all the variables

5(w-3)7w+21=0

We multiply parentheses

35w^2-105w+21=0

a = 35; b = -105; c = +21;
Δ = b2-4ac
Δ = -1052-4·35·21
Δ = 8085
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8085}=\sqrt{49*165}=\sqrt{49}*\sqrt{165}=7\sqrt{165}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-105)-7\sqrt{165}}{2*35}=\frac{105-7\sqrt{165}}{70}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-105)+7\sqrt{165}}{2*35}=\frac{105+7\sqrt{165}}{70}
$