10x^2-84x+12=0

Solution for 10x^2-84x+12=0 equation:

10x^2-84x+12=0

a = 10; b = -84; c = +12;
Δ = b2-4ac
Δ = -842-4·10·12
Δ = 6576
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:

$\sqrt{\Delta}=\sqrt{6576}=\sqrt{16*411}=\sqrt{16}*\sqrt{411}=4\sqrt{411}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{411}}{2*10}=\frac{84-4\sqrt{411}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{411}}{2*10}=\frac{84+4\sqrt{411}}{20}
$