3x-15=1/2x-5

Solution for 3x-15=1/2x-5 equation:

3x-15=1/2x-5

We move all terms to the left:

3x-15-(1/2x-5)=0


Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

3x-1/2x+5-15=0

We multiply all the terms by the denominator


3x*2x+5*2x-15*2x-1=0

Wy multiply elements

6x^2+10x-30x-1=0

We add all the numbers together, and all the variables

6x^2-20x-1=0

a = 6; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·6·(-1)
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{106}}{2*6}=\frac{20-2\sqrt{106}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{106}}{2*6}=\frac{20+2\sqrt{106}}{12}
$