17x^2-82x+24=0

Solution for 17x^2-82x+24=0 equation:

17x^2-82x+24=0

a = 17; b = -82; c = +24;
Δ = b2-4ac
Δ = -822-4·17·24
Δ = 5092
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:

$\sqrt{\Delta}=\sqrt{5092}=\sqrt{4*1273}=\sqrt{4}*\sqrt{1273}=2\sqrt{1273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{1273}}{2*17}=\frac{82-2\sqrt{1273}}{34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{1273}}{2*17}=\frac{82+2\sqrt{1273}}{34}
$