3x2-74x+24=0

Solution for 3x2-74x+24=0 equation:

3x^2-74x+24=0

a = 3; b = -74; c = +24;
Δ = b2-4ac
Δ = -742-4·3·24
Δ = 5188
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:

$\sqrt{\Delta}=\sqrt{5188}=\sqrt{4*1297}=\sqrt{4}*\sqrt{1297}=2\sqrt{1297}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-74)-2\sqrt{1297}}{2*3}=\frac{74-2\sqrt{1297}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-74)+2\sqrt{1297}}{2*3}=\frac{74+2\sqrt{1297}}{6}
$