8x^2-168x+405=0

Solution for 8x^2-168x+405=0 equation:

8x^2-168x+405=0

a = 8; b = -168; c = +405;
Δ = b2-4ac
Δ = -1682-4·8·405
Δ = 15264
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:

$\sqrt{\Delta}=\sqrt{15264}=\sqrt{144*106}=\sqrt{144}*\sqrt{106}=12\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-168)-12\sqrt{106}}{2*8}=\frac{168-12\sqrt{106}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-168)+12\sqrt{106}}{2*8}=\frac{168+12\sqrt{106}}{16}
$