5x^2+14x-9=0

Solution for 5x^2+14x-9=0 equation:

5x^2+14x-9=0

a = 5; b = 14; c = -9;
Δ = b2-4ac
Δ = 142-4·5·(-9)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{94}}{2*5}=\frac{-14-2\sqrt{94}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{94}}{2*5}=\frac{-14+2\sqrt{94}}{10}
$