5x^2+15x-9=0

Solution for 5x^2+15x-9=0 equation:

5x^2+15x-9=0

a = 5; b = 15; c = -9;
Δ = b2-4ac
Δ = 152-4·5·(-9)
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9\sqrt{5}}{2*5}=\frac{-15-9\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9\sqrt{5}}{2*5}=\frac{-15+9\sqrt{5}}{10}
$