3x^2-75x+200=0

Solution for 3x^2-75x+200=0 equation:

3x^2-75x+200=0

a = 3; b = -75; c = +200;
Δ = b2-4ac
Δ = -752-4·3·200
Δ = 3225
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:

$\sqrt{\Delta}=\sqrt{3225}=\sqrt{25*129}=\sqrt{25}*\sqrt{129}=5\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{129}}{2*3}=\frac{75-5\sqrt{129}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{129}}{2*3}=\frac{75+5\sqrt{129}}{6}
$