84*x^2-x-20=0

Solution for 84*x^2-x-20=0 equation:

84x^2-x-20=0

We add all the numbers together, and all the variables

84x^2-1x-20=0

a = 84; b = -1; c = -20;
Δ = b2-4ac
Δ = -12-4·84·(-20)
Δ = 6721
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{6721}}{2*84}=\frac{1-\sqrt{6721}}{168}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{6721}}{2*84}=\frac{1+\sqrt{6721}}{168}
$