x+7/12x+7=12.5

Solution for x+7/12x+7=12.5 equation:

x+7/12x+7=12.5

We move all terms to the left:

x+7/12x+7-(12.5)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R


We add all the numbers together, and all the variables

x+7/12x-5.5=0

We multiply all the terms by the denominator


x*12x-(5.5)*12x+7=0

We multiply parentheses

x*12x-66x+7=0

Wy multiply elements

12x^2-66x+7=0

a = 12; b = -66; c = +7;
Δ = b2-4ac
Δ = -662-4·12·7
Δ = 4020
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:

$\sqrt{\Delta}=\sqrt{4020}=\sqrt{4*1005}=\sqrt{4}*\sqrt{1005}=2\sqrt{1005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1005}}{2*12}=\frac{66-2\sqrt{1005}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1005}}{2*12}=\frac{66+2\sqrt{1005}}{24}
$