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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


(.5x)*2x-2*2x+4*2x-3=0

We add all the numbers together, and all the variables

(+.5x)*2x-2*2x+4*2x-3=0

We multiply parentheses

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

Wy multiply elements

2x^2-4x+8x-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}
$