17x^2+8x-42=0

Solution for 17x^2+8x-42=0 equation:

17x^2+8x-42=0

a = 17; b = 8; c = -42;
Δ = b2-4ac
Δ = 82-4·17·(-42)
Δ = 2920
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:

$\sqrt{\Delta}=\sqrt{2920}=\sqrt{4*730}=\sqrt{4}*\sqrt{730}=2\sqrt{730}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{730}}{2*17}=\frac{-8-2\sqrt{730}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{730}}{2*17}=\frac{-8+2\sqrt{730}}{34}
$