0.5x=-3/2x+4

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

0.5x=-3/2x+4

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

0.5x+3/2x-4=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

Wy multiply elements

0x^2-8x+3=0

We add all the numbers together, and all the variables

x^2-8x+3=0

a = 1; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·1·3
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{13}}{2*1}=\frac{8-2\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{13}}{2*1}=\frac{8+2\sqrt{13}}{2}
$