10y(y+3)=51

Solution for 10y(y+3)=51 equation:

10y(y+3)=51

We move all terms to the left:

10y(y+3)-(51)=0

We multiply parentheses

10y^2+30y-51=0

a = 10; b = 30; c = -51;
Δ = b2-4ac
Δ = 302-4·10·(-51)
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-14\sqrt{15}}{2*10}=\frac{-30-14\sqrt{15}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+14\sqrt{15}}{2*10}=\frac{-30+14\sqrt{15}}{20}
$