8x^2-3x-459=0

Solution for 8x^2-3x-459=0 equation:

8x^2-3x-459=0

a = 8; b = -3; c = -459;
Δ = b2-4ac
Δ = -32-4·8·(-459)
Δ = 14697
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:

$\sqrt{\Delta}=\sqrt{14697}=\sqrt{9*1633}=\sqrt{9}*\sqrt{1633}=3\sqrt{1633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{1633}}{2*8}=\frac{3-3\sqrt{1633}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{1633}}{2*8}=\frac{3+3\sqrt{1633}}{16}
$