3x=1/2x+95

Solution for 3x=1/2x+95 equation:

3x=1/2x+95

We move all terms to the left:

3x-(1/2x+95)=0


Domain of the equation: 2x+95)!=0

x∈R


We get rid of parentheses

3x-1/2x-95=0

We multiply all the terms by the denominator


3x*2x-95*2x-1=0

Wy multiply elements

6x^2-190x-1=0

a = 6; b = -190; c = -1;
Δ = b2-4ac
Δ = -1902-4·6·(-1)
Δ = 36124
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:

$\sqrt{\Delta}=\sqrt{36124}=\sqrt{4*9031}=\sqrt{4}*\sqrt{9031}=2\sqrt{9031}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-190)-2\sqrt{9031}}{2*6}=\frac{190-2\sqrt{9031}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-190)+2\sqrt{9031}}{2*6}=\frac{190+2\sqrt{9031}}{12}
$