5w(w-6)=7w-30

Solution for 5w(w-6)=7w-30 equation:

5w(w-6)=7w-30

We move all terms to the left:

5w(w-6)-(7w-30)=0

We multiply parentheses

5w^2-30w-(7w-30)=0

We get rid of parentheses

5w^2-30w-7w+30=0

We add all the numbers together, and all the variables

5w^2-37w+30=0

a = 5; b = -37; c = +30;
Δ = b2-4ac
Δ = -372-4·5·30
Δ = 769
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{-(-37)-\sqrt{769}}{2*5}=\frac{37-\sqrt{769}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{769}}{2*5}=\frac{37+\sqrt{769}}{10}
$