3x^2=(18)3/4

Solution for 3x^2=(18)3/4 equation:

3x^2=(18)3/4

We move all terms to the left:

3x^2-((18)3/4)=0

We add all the numbers together, and all the variables

3x^2-(+183/4)=0

We get rid of parentheses

3x^2-183/4=0

We multiply all the terms by the denominator


3x^2*4-183=0

Wy multiply elements

12x^2-183=0

a = 12; b = 0; c = -183;
Δ = b2-4ac
Δ = 02-4·12·(-183)
Δ = 8784
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:

$\sqrt{\Delta}=\sqrt{8784}=\sqrt{144*61}=\sqrt{144}*\sqrt{61}=12\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{61}}{2*12}=\frac{0-12\sqrt{61}}{24}
=-\frac{12\sqrt{61}}{24}
=-\frac{\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{61}}{2*12}=\frac{0+12\sqrt{61}}{24}
=\frac{12\sqrt{61}}{24}
=\frac{\sqrt{61}}{2}
$