3/2x+14=24-x

Solution for 3/2x+14=24-x equation:

3/2x+14=24-x

We move all terms to the left:

3/2x+14-(24-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x-(-1x+24)+14=0

We get rid of parentheses

3/2x+1x-24+14=0

We multiply all the terms by the denominator


1x*2x-24*2x+14*2x+3=0

Wy multiply elements

2x^2-48x+28x+3=0

We add all the numbers together, and all the variables

2x^2-20x+3=0

a = 2; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·2·3
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{94}}{2*2}=\frac{20-2\sqrt{94}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{94}}{2*2}=\frac{20+2\sqrt{94}}{4}
$