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

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

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

We move all terms to the left:

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

We multiply parentheses

-3w^2+21w-(5w+3)=0

We get rid of parentheses

-3w^2+21w-5w-3=0

We add all the numbers together, and all the variables

-3w^2+16w-3=0

a = -3; b = 16; c = -3;
Δ = b2-4ac
Δ = 162-4·(-3)·(-3)
Δ = 220
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:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{55}}{2*-3}=\frac{-16-2\sqrt{55}}{-6}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{55}}{2*-3}=\frac{-16+2\sqrt{55}}{-6}
$