5w(7w-)=10w+1

Solution for 5w(7w-)=10w+1 equation:

5w(7w-)=10w+1

We move all terms to the left:

5w(7w-)-(10w+1)=0

We add all the numbers together, and all the variables

5w(+7w)-(10w+1)=0

We multiply parentheses

35w^2-(10w+1)=0

We get rid of parentheses

35w^2-10w-1=0

a = 35; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·35·(-1)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-4\sqrt{15}}{2*35}=\frac{10-4\sqrt{15}}{70}
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+4\sqrt{15}}{2*35}=\frac{10+4\sqrt{15}}{70}
$