(5w+1)(7w-7)=180

Solution for (5w+1)(7w-7)=180 equation:

(5w+1)(7w-7)=180

We move all terms to the left:

(5w+1)(7w-7)-(180)=0

We multiply parentheses ..

(+35w^2-35w+7w-7)-180=0

We get rid of parentheses

35w^2-35w+7w-7-180=0

We add all the numbers together, and all the variables

35w^2-28w-187=0

a = 35; b = -28; c = -187;
Δ = b2-4ac
Δ = -282-4·35·(-187)
Δ = 26964
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:

$\sqrt{\Delta}=\sqrt{26964}=\sqrt{36*749}=\sqrt{36}*\sqrt{749}=6\sqrt{749}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-6\sqrt{749}}{2*35}=\frac{28-6\sqrt{749}}{70}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+6\sqrt{749}}{2*35}=\frac{28+6\sqrt{749}}{70}
$