4(2x-3)/2x=10x-12

Solution for 4(2x-3)/2x=10x-12 equation:

4(2x-3)/2x=10x-12

We move all terms to the left:

4(2x-3)/2x-(10x-12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

4(2x-3)/2x-10x+12=0

We multiply all the terms by the denominator


4(2x-3)-10x*2x+12*2x=0

We multiply parentheses

8x-10x*2x+12*2x-12=0

Wy multiply elements

-20x^2+8x+24x-12=0

We add all the numbers together, and all the variables

-20x^2+32x-12=0

a = -20; b = 32; c = -12;
Δ = b2-4ac
Δ = 322-4·(-20)·(-12)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-8}{2*-20}=\frac{-40}{-40}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+8}{2*-20}=\frac{-24}{-40}
=3/5
$