1/2x=3x-130

Solution for 1/2x=3x-130 equation:

1/2x=3x-130

We move all terms to the left:

1/2x-(3x-130)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-3x+130=0

We multiply all the terms by the denominator


-3x*2x+130*2x+1=0

Wy multiply elements

-6x^2+260x+1=0

a = -6; b = 260; c = +1;
Δ = b2-4ac
Δ = 2602-4·(-6)·1
Δ = 67624
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:

$\sqrt{\Delta}=\sqrt{67624}=\sqrt{4*16906}=\sqrt{4}*\sqrt{16906}=2\sqrt{16906}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(260)-2\sqrt{16906}}{2*-6}=\frac{-260-2\sqrt{16906}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(260)+2\sqrt{16906}}{2*-6}=\frac{-260+2\sqrt{16906}}{-12}
$