54x^2+200-300=0

Solution for 54x^2+200-300=0 equation:

54x^2+200-300=0

We add all the numbers together, and all the variables

54x^2-100=0

a = 54; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·54·(-100)
Δ = 21600
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:

$\sqrt{\Delta}=\sqrt{21600}=\sqrt{3600*6}=\sqrt{3600}*\sqrt{6}=60\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60\sqrt{6}}{2*54}=\frac{0-60\sqrt{6}}{108}
=-\frac{60\sqrt{6}}{108}
=-\frac{5\sqrt{6}}{9}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{6}}{2*54}=\frac{0+60\sqrt{6}}{108}
=\frac{60\sqrt{6}}{108}
=\frac{5\sqrt{6}}{9}
$