3/2*x=180

Solution for 3/2*x=180 equation:

3/2*x=180

We move all terms to the left:

3/2*x-(180)=0


Domain of the equation: 2*x!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-180*2*x+3=0

Wy multiply elements

-360x*x+3=0

Wy multiply elements

-360x^2+3=0

a = -360; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-360)·3
Δ = 4320
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:

$\sqrt{\Delta}=\sqrt{4320}=\sqrt{144*30}=\sqrt{144}*\sqrt{30}=12\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{30}}{2*-360}=\frac{0-12\sqrt{30}}{-720}
=-\frac{12\sqrt{30}}{-720}
=-\frac{\sqrt{30}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{30}}{2*-360}=\frac{0+12\sqrt{30}}{-720}
=\frac{12\sqrt{30}}{-720}
=\frac{\sqrt{30}}{-60}
$