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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

4x+3/2x-(3x+5)-12=0

We get rid of parentheses

4x+3/2x-3x-5-12=0

We multiply all the terms by the denominator


4x*2x-3x*2x-5*2x-12*2x+3=0

Wy multiply elements

8x^2-6x^2-10x-24x+3=0

We add all the numbers together, and all the variables

2x^2-34x+3=0

a = 2; b = -34; c = +3;
Δ = b2-4ac
Δ = -342-4·2·3
Δ = 1132
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:

$\sqrt{\Delta}=\sqrt{1132}=\sqrt{4*283}=\sqrt{4}*\sqrt{283}=2\sqrt{283}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-2\sqrt{283}}{2*2}=\frac{34-2\sqrt{283}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+2\sqrt{283}}{2*2}=\frac{34+2\sqrt{283}}{4}
$