34y^2+8y-119=0

Solution for 34y^2+8y-119=0 equation:

34y^2+8y-119=0

a = 34; b = 8; c = -119;
Δ = b2-4ac
Δ = 82-4·34·(-119)
Δ = 16248
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{16248}=\sqrt{4*4062}=\sqrt{4}*\sqrt{4062}=2\sqrt{4062}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{4062}}{2*34}=\frac{-8-2\sqrt{4062}}{68}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{4062}}{2*34}=\frac{-8+2\sqrt{4062}}{68}
$