10y^2+8y-9=0

Solution for 10y^2+8y-9=0 equation:

10y^2+8y-9=0

a = 10; b = 8; c = -9;
Δ = b2-4ac
Δ = 82-4·10·(-9)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{106}}{2*10}=\frac{-8-2\sqrt{106}}{20}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{106}}{2*10}=\frac{-8+2\sqrt{106}}{20}
$