17x^2+6x-25=0

Solution for 17x^2+6x-25=0 equation:

17x^2+6x-25=0

a = 17; b = 6; c = -25;
Δ = b2-4ac
Δ = 62-4·17·(-25)
Δ = 1736
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:

$\sqrt{\Delta}=\sqrt{1736}=\sqrt{4*434}=\sqrt{4}*\sqrt{434}=2\sqrt{434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{434}}{2*17}=\frac{-6-2\sqrt{434}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{434}}{2*17}=\frac{-6+2\sqrt{434}}{34}
$