(5w+2)(w-1)=3w+1

Solution for (5w+2)(w-1)=3w+1 equation:

(5w+2)(w-1)=3w+1

We move all terms to the left:

(5w+2)(w-1)-(3w+1)=0

We get rid of parentheses

(5w+2)(w-1)-3w-1=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5w^2-6w-3=0

a = 5; b = -6; c = -3;
Δ = b2-4ac
Δ = -62-4·5·(-3)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-4\sqrt{6}}{2*5}=\frac{6-4\sqrt{6}}{10}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+4\sqrt{6}}{2*5}=\frac{6+4\sqrt{6}}{10}
$