10r^2-4r-9=0

Solution for 10r^2-4r-9=0 equation:

10r^2-4r-9=0

a = 10; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·10·(-9)
Δ = 376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{94}}{2*10}=\frac{4-2\sqrt{94}}{20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{94}}{2*10}=\frac{4+2\sqrt{94}}{20}
$