x=12/x+5=3/2

Solution for x=12/x+5=3/2 equation:

x=12/x+5=3/2

We move all terms to the left:

x-(12/x+5)=0


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

x∈R


We get rid of parentheses

x-12/x-5=0

We multiply all the terms by the denominator


x*x-5*x-12=0

We add all the numbers together, and all the variables

-5x+x*x-12=0

Wy multiply elements

x^2-5x-12=0

a = 1; b = -5; c = -12;
Δ = b2-4ac
Δ = -52-4·1·(-12)
Δ = 73
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{-(-5)-\sqrt{73}}{2*1}=\frac{5-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*1}=\frac{5+\sqrt{73}}{2}
$