3x^2-84x+69=0

Solution for 3x^2-84x+69=0 equation:

3x^2-84x+69=0

a = 3; b = -84; c = +69;
Δ = b2-4ac
Δ = -842-4·3·69
Δ = 6228
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:

$\sqrt{\Delta}=\sqrt{6228}=\sqrt{36*173}=\sqrt{36}*\sqrt{173}=6\sqrt{173}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-6\sqrt{173}}{2*3}=\frac{84-6\sqrt{173}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+6\sqrt{173}}{2*3}=\frac{84+6\sqrt{173}}{6}
$