14x2+16x-17=0

Solution for 14x2+16x-17=0 equation:

14x^2+16x-17=0

a = 14; b = 16; c = -17;
Δ = b2-4ac
Δ = 162-4·14·(-17)
Δ = 1208
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:

$\sqrt{\Delta}=\sqrt{1208}=\sqrt{4*302}=\sqrt{4}*\sqrt{302}=2\sqrt{302}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{302}}{2*14}=\frac{-16-2\sqrt{302}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{302}}{2*14}=\frac{-16+2\sqrt{302}}{28}
$