17x^2-106x+160=0

Solution for 17x^2-106x+160=0 equation:

17x^2-106x+160=0

a = 17; b = -106; c = +160;
Δ = b2-4ac
Δ = -1062-4·17·160
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-106)-2\sqrt{89}}{2*17}=\frac{106-2\sqrt{89}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-106)+2\sqrt{89}}{2*17}=\frac{106+2\sqrt{89}}{34}
$