-10x^2+10x+9=0

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

-10x^2+10x+9=0

a = -10; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-10)·9
Δ = 460
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{115}}{2*-10}=\frac{-10-2\sqrt{115}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{115}}{2*-10}=\frac{-10+2\sqrt{115}}{-20}
$