25y^2+15y=21

Solution for 25y^2+15y=21 equation:

25y^2+15y=21

We move all terms to the left:

25y^2+15y-(21)=0

a = 25; b = 15; c = -21;
Δ = b2-4ac
Δ = 152-4·25·(-21)
Δ = 2325
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:

$\sqrt{\Delta}=\sqrt{2325}=\sqrt{25*93}=\sqrt{25}*\sqrt{93}=5\sqrt{93}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{93}}{2*25}=\frac{-15-5\sqrt{93}}{50}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{93}}{2*25}=\frac{-15+5\sqrt{93}}{50}
$