84+2x-6x^2=0

Solution for 84+2x-6x^2=0 equation:

84+2x-6x^2=0

a = -6; b = 2; c = +84;
Δ = b2-4ac
Δ = 22-4·(-6)·84
Δ = 2020
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:

$\sqrt{\Delta}=\sqrt{2020}=\sqrt{4*505}=\sqrt{4}*\sqrt{505}=2\sqrt{505}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{505}}{2*-6}=\frac{-2-2\sqrt{505}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{505}}{2*-6}=\frac{-2+2\sqrt{505}}{-12}
$