15x^2-80x+84=0

Solution for 15x^2-80x+84=0 equation:

15x^2-80x+84=0

a = 15; b = -80; c = +84;
Δ = b2-4ac
Δ = -802-4·15·84
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-4\sqrt{85}}{2*15}=\frac{80-4\sqrt{85}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+4\sqrt{85}}{2*15}=\frac{80+4\sqrt{85}}{30}
$