x=12/2x+5

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

x=12/2x+5

We move all terms to the left:

x-(12/2x+5)=0


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

x-12/2x-5=0

We multiply all the terms by the denominator


x*2x-5*2x-12=0

Wy multiply elements

2x^2-10x-12=0

a = 2; b = -10; c = -12;
Δ = b2-4ac
Δ = -102-4·2·(-12)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*2}=\frac{24}{4}
=6
$