3x^2-300=50x

Solution for 3x^2-300=50x equation:

3x^2-300=50x

We move all terms to the left:

3x^2-300-(50x)=0

a = 3; b = -50; c = -300;
Δ = b2-4ac
Δ = -502-4·3·(-300)
Δ = 6100
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:

$\sqrt{\Delta}=\sqrt{6100}=\sqrt{100*61}=\sqrt{100}*\sqrt{61}=10\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{61}}{2*3}=\frac{50-10\sqrt{61}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{61}}{2*3}=\frac{50+10\sqrt{61}}{6}
$