1/3*x*12=150

Solution for 1/3*x*12=150 equation:

1/3*x*12=150

We move all terms to the left:

1/3*x*12-(150)=0


Domain of the equation: 3*x*12!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-150*3*x*12+1=0

Wy multiply elements

-5400x*x+1=0

Wy multiply elements

-5400x^2+1=0

a = -5400; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-5400)·1
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*-5400}=\frac{0-60\sqrt{6}}{-10800}
=-\frac{60\sqrt{6}}{-10800}
=-\frac{\sqrt{6}}{-180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60\sqrt{6}}{2*-5400}=\frac{0+60\sqrt{6}}{-10800}
=\frac{60\sqrt{6}}{-10800}
=\frac{\sqrt{6}}{-180}
$