10y^2+21y-126=0

Solution for 10y^2+21y-126=0 equation:

10y^2+21y-126=0

a = 10; b = 21; c = -126;
Δ = b2-4ac
Δ = 212-4·10·(-126)
Δ = 5481
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:

$\sqrt{\Delta}=\sqrt{5481}=\sqrt{9*609}=\sqrt{9}*\sqrt{609}=3\sqrt{609}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{609}}{2*10}=\frac{-21-3\sqrt{609}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{609}}{2*10}=\frac{-21+3\sqrt{609}}{20}
$