0.5x+4=3/2x+2

Solution for 0.5x+4=3/2x+2 equation:

0.5x+4=3/2x+2

We move all terms to the left:

0.5x+4-(3/2x+2)=0


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

x∈R


We get rid of parentheses

0.5x-3/2x-2+4=0

We multiply all the terms by the denominator


(0.5x)*2x-2*2x+4*2x-3=0

We add all the numbers together, and all the variables

(+0.5x)*2x-2*2x+4*2x-3=0

We multiply parentheses

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

Wy multiply elements

0x^2-4x+8x-3=0

We add all the numbers together, and all the variables

x^2+4x-3=0

a = 1; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·1·(-3)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{7}}{2*1}=\frac{-4-2\sqrt{7}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{7}}{2*1}=\frac{-4+2\sqrt{7}}{2}
$