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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1w+(5w-3)(w+5)=0

We multiply parentheses ..

(+5w^2+25w-3w-15)-1w=0

We get rid of parentheses

5w^2+25w-3w-1w-15=0

We add all the numbers together, and all the variables

5w^2+21w-15=0

a = 5; b = 21; c = -15;
Δ = b2-4ac
Δ = 212-4·5·(-15)
Δ = 741
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{-(21)-\sqrt{741}}{2*5}=\frac{-21-\sqrt{741}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+\sqrt{741}}{2*5}=\frac{-21+\sqrt{741}}{10}
$