10x-1=1/2x-3

Solution for 10x-1=1/2x-3 equation:

10x-1=1/2x-3

We move all terms to the left:

10x-1-(1/2x-3)=0


Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

10x-1/2x+3-1=0

We multiply all the terms by the denominator


10x*2x+3*2x-1*2x-1=0

Wy multiply elements

20x^2+6x-2x-1=0

We add all the numbers together, and all the variables

20x^2+4x-1=0

a = 20; b = 4; c = -1;
Δ = b2-4ac
Δ = 42-4·20·(-1)
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*20}=\frac{-4-4\sqrt{6}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*20}=\frac{-4+4\sqrt{6}}{40}
$