0.5x-4=1/3x+5

Solution for 0.5x-4=1/3x+5 equation:

0.5x-4=1/3x+5

We move all terms to the left:

0.5x-4-(1/3x+5)=0


Domain of the equation: 3x+5)!=0

x∈R


We get rid of parentheses

0.5x-1/3x-5-4=0

We multiply all the terms by the denominator


(0.5x)*3x-5*3x-4*3x-1=0

We add all the numbers together, and all the variables

(+0.5x)*3x-5*3x-4*3x-1=0

We multiply parentheses

0x^2-5*3x-4*3x-1=0

Wy multiply elements

0x^2-15x-12x-1=0

We add all the numbers together, and all the variables

x^2-27x-1=0

a = 1; b = -27; c = -1;
Δ = b2-4ac
Δ = -272-4·1·(-1)
Δ = 733
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-\sqrt{733}}{2*1}=\frac{27-\sqrt{733}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{733}}{2*1}=\frac{27+\sqrt{733}}{2}
$