5y(y-3)=35

Solution for 5y(y-3)=35 equation:

5y(y-3)=35

We move all terms to the left:

5y(y-3)-(35)=0

We multiply parentheses

5y^2-15y-35=0

a = 5; b = -15; c = -35;
Δ = b2-4ac
Δ = -152-4·5·(-35)
Δ = 925
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{925}=\sqrt{25*37}=\sqrt{25}*\sqrt{37}=5\sqrt{37}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{37}}{2*5}=\frac{15-5\sqrt{37}}{10}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{37}}{2*5}=\frac{15+5\sqrt{37}}{10}
$