3x^2-5x-200=0

Solution for 3x^2-5x-200=0 equation:

3x^2-5x-200=0

a = 3; b = -5; c = -200;
Δ = b2-4ac
Δ = -52-4·3·(-200)
Δ = 2425
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:

$\sqrt{\Delta}=\sqrt{2425}=\sqrt{25*97}=\sqrt{25}*\sqrt{97}=5\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{97}}{2*3}=\frac{5-5\sqrt{97}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{97}}{2*3}=\frac{5+5\sqrt{97}}{6}
$