3x^2+75x-84=0

Solution for 3x^2+75x-84=0 equation:

3x^2+75x-84=0

a = 3; b = 75; c = -84;
Δ = b2-4ac
Δ = 752-4·3·(-84)
Δ = 6633
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:

$\sqrt{\Delta}=\sqrt{6633}=\sqrt{9*737}=\sqrt{9}*\sqrt{737}=3\sqrt{737}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-3\sqrt{737}}{2*3}=\frac{-75-3\sqrt{737}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+3\sqrt{737}}{2*3}=\frac{-75+3\sqrt{737}}{6}
$