(3x)(1/2x)+90=180

Solution for (3x)(1/2x)+90=180 equation:

(3x)(1/2x)+90=180

We move all terms to the left:

(3x)(1/2x)+90-(180)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x(+1/2x)+90-180=0

We add all the numbers together, and all the variables

3x(+1/2x)-90=0

We multiply parentheses

3x^2-90=0

a = 3; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·3·(-90)
Δ = 1080
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:

$\sqrt{\Delta}=\sqrt{1080}=\sqrt{36*30}=\sqrt{36}*\sqrt{30}=6\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{30}}{2*3}=\frac{0-6\sqrt{30}}{6}
=-\frac{6\sqrt{30}}{6}
=-\sqrt{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{30}}{2*3}=\frac{0+6\sqrt{30}}{6}
=\frac{6\sqrt{30}}{6}
=\sqrt{30}
$