x=3+5+4+3/2x

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

x=3+5+4+3/2x

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

x-3/2x-12=0

We multiply all the terms by the denominator


x*2x-12*2x-3=0

Wy multiply elements

2x^2-24x-3=0

a = 2; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·2·(-3)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-10\sqrt{6}}{2*2}=\frac{24-10\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+10\sqrt{6}}{2*2}=\frac{24+10\sqrt{6}}{4}
$