100=48x+12/x+2

Solution for 100=48x+12/x+2 equation:

100=48x+12/x+2

We move all terms to the left:

100-(48x+12/x+2)=0


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

x∈R


We get rid of parentheses

-48x-12/x-2+100=0

We multiply all the terms by the denominator


-48x*x-2*x+100*x-12=0

We add all the numbers together, and all the variables

98x-48x*x-12=0

Wy multiply elements

-48x^2+98x-12=0

a = -48; b = 98; c = -12;
Δ = b2-4ac
Δ = 982-4·(-48)·(-12)
Δ = 7300
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:

$\sqrt{\Delta}=\sqrt{7300}=\sqrt{100*73}=\sqrt{100}*\sqrt{73}=10\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-10\sqrt{73}}{2*-48}=\frac{-98-10\sqrt{73}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+10\sqrt{73}}{2*-48}=\frac{-98+10\sqrt{73}}{-96}
$