(x^2/54)=190

Solution for (x^2/54)=190 equation:

(x^2/54)=190

We move all terms to the left:

(x^2/54)-(190)=0

We get rid of parentheses

x^2/54-190=0

We multiply all the terms by the denominator


x^2-190*54=0

We add all the numbers together, and all the variables

x^2-10260=0

a = 1; b = 0; c = -10260;
Δ = b2-4ac
Δ = 02-4·1·(-10260)
Δ = 41040
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:

$\sqrt{\Delta}=\sqrt{41040}=\sqrt{144*285}=\sqrt{144}*\sqrt{285}=12\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{285}}{2*1}=\frac{0-12\sqrt{285}}{2}
=-\frac{12\sqrt{285}}{2}
=-6\sqrt{285}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{285}}{2*1}=\frac{0+12\sqrt{285}}{2}
=\frac{12\sqrt{285}}{2}
=6\sqrt{285}
$