(3x-5)=1/2(4x)

Solution for (3x-5)=1/2(4x) equation:

(3x-5)=1/2(4x)

We move all terms to the left:

(3x-5)-(1/2(4x))=0


Domain of the equation: 24x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(3x-5)-(+1/24x)=0

We get rid of parentheses

3x-1/24x-5=0

We multiply all the terms by the denominator


3x*24x-5*24x-1=0

Wy multiply elements

72x^2-120x-1=0

a = 72; b = -120; c = -1;
Δ = b2-4ac
Δ = -1202-4·72·(-1)
Δ = 14688
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:

$\sqrt{\Delta}=\sqrt{14688}=\sqrt{144*102}=\sqrt{144}*\sqrt{102}=12\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-12\sqrt{102}}{2*72}=\frac{120-12\sqrt{102}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+12\sqrt{102}}{2*72}=\frac{120+12\sqrt{102}}{144}
$