5w(w-1)-2=5w+7

Solution for 5w(w-1)-2=5w+7 equation:

5w(w-1)-2=5w+7

We move all terms to the left:

5w(w-1)-2-(5w+7)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5w^2-10w-9=0

a = 5; b = -10; c = -9;
Δ = b2-4ac
Δ = -102-4·5·(-9)
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{70}}{2*5}=\frac{10-2\sqrt{70}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{70}}{2*5}=\frac{10+2\sqrt{70}}{10}
$