3x+24/2x+16=1,5

Solution for 3x+24/2x+16=1,5 equation:

3x+24/2x+16=1.5

We move all terms to the left:

3x+24/2x+16-(1.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x+24/2x+14.5=0

We multiply all the terms by the denominator


3x*2x+(14.5)*2x+24=0

We multiply parentheses

3x*2x+29x+24=0

Wy multiply elements

6x^2+29x+24=0

a = 6; b = 29; c = +24;
Δ = b2-4ac
Δ = 292-4·6·24
Δ = 265
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{-(29)-\sqrt{265}}{2*6}=\frac{-29-\sqrt{265}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{265}}{2*6}=\frac{-29+\sqrt{265}}{12}
$