4x-3=2/3x-23

Solution for 4x-3=2/3x-23 equation:

4x-3=2/3x-23

We move all terms to the left:

4x-3-(2/3x-23)=0


Domain of the equation: 3x-23)!=0

x∈R


We get rid of parentheses

4x-2/3x+23-3=0

We multiply all the terms by the denominator


4x*3x+23*3x-3*3x-2=0

Wy multiply elements

12x^2+69x-9x-2=0

We add all the numbers together, and all the variables

12x^2+60x-2=0

a = 12; b = 60; c = -2;
Δ = b2-4ac
Δ = 602-4·12·(-2)
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-4\sqrt{231}}{2*12}=\frac{-60-4\sqrt{231}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+4\sqrt{231}}{2*12}=\frac{-60+4\sqrt{231}}{24}
$