x+6=3/2x+4

Solution for x+6=3/2x+4 equation:

x+6=3/2x+4

We move all terms to the left:

x+6-(3/2x+4)=0


Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

x-3/2x-4+6=0

We multiply all the terms by the denominator


x*2x-4*2x+6*2x-3=0

Wy multiply elements

2x^2-8x+12x-3=0

We add all the numbers together, and all the variables

2x^2+4x-3=0

a = 2; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·2·(-3)
Δ = 40
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:

$\sqrt{\Delta}=\sqrt{40}=\sqrt{4*10}=\sqrt{4}*\sqrt{10}=2\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{10}}{2*2}=\frac{-4-2\sqrt{10}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{10}}{2*2}=\frac{-4+2\sqrt{10}}{4}
$