1/2x=2x-30=180

Solution for 1/2x=2x-30=180 equation:

1/2x=2x-30=180

We move all terms to the left:

1/2x-(2x-30)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-2x+30=0

We multiply all the terms by the denominator


-2x*2x+30*2x+1=0

Wy multiply elements

-4x^2+60x+1=0

a = -4; b = 60; c = +1;
Δ = b2-4ac
Δ = 602-4·(-4)·1
Δ = 3616
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:

$\sqrt{\Delta}=\sqrt{3616}=\sqrt{16*226}=\sqrt{16}*\sqrt{226}=4\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{226}}{2*-4}=\frac{-60-4\sqrt{226}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{226}}{2*-4}=\frac{-60+4\sqrt{226}}{-8}
$