0.5x-3=3/2x+4

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

0.5x-3=3/2x+4

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

Wy multiply elements

0x^2-8x-6x-3=0

We add all the numbers together, and all the variables

x^2-14x-3=0

a = 1; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·1·(-3)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{13}}{2*1}=\frac{14-4\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{13}}{2*1}=\frac{14+4\sqrt{13}}{2}
$