5/6x^2-12=18

Solution for 5/6x^2-12=18 equation:

5/6x^2-12=18

We move all terms to the left:

5/6x^2-12-(18)=0


Domain of the equation: 6x^2!=0

x^2!=0/6

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

5/6x^2-30=0

We multiply all the terms by the denominator


-30*6x^2+5=0

Wy multiply elements

-180x^2+5=0

a = -180; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-180)·5
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*-180}=\frac{-60}{-360}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*-180}=\frac{60}{-360}
=-1/6
$