9/2x+4=48-x

Solution for 9/2x+4=48-x equation:

9/2x+4=48-x

We move all terms to the left:

9/2x+4-(48-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

9/2x-(-1x+48)+4=0

We get rid of parentheses

9/2x+1x-48+4=0

We multiply all the terms by the denominator


1x*2x-48*2x+4*2x+9=0

Wy multiply elements

2x^2-96x+8x+9=0

We add all the numbers together, and all the variables

2x^2-88x+9=0

a = 2; b = -88; c = +9;
Δ = b2-4ac
Δ = -882-4·2·9
Δ = 7672
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:

$\sqrt{\Delta}=\sqrt{7672}=\sqrt{4*1918}=\sqrt{4}*\sqrt{1918}=2\sqrt{1918}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-88)-2\sqrt{1918}}{2*2}=\frac{88-2\sqrt{1918}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-88)+2\sqrt{1918}}{2*2}=\frac{88+2\sqrt{1918}}{4}
$