3x^2-300=50

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

3x^2-300=50

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-350=0

a = 3; b = 0; c = -350;
Δ = b2-4ac
Δ = 02-4·3·(-350)
Δ = 4200
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:

$\sqrt{\Delta}=\sqrt{4200}=\sqrt{100*42}=\sqrt{100}*\sqrt{42}=10\sqrt{42}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{42}}{2*3}=\frac{0-10\sqrt{42}}{6}
=-\frac{10\sqrt{42}}{6}
=-\frac{5\sqrt{42}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{42}}{2*3}=\frac{0+10\sqrt{42}}{6}
=\frac{10\sqrt{42}}{6}
=\frac{5\sqrt{42}}{3}
$