x+7/12x+7=12

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

x+7/12x+7=12

We move all terms to the left:

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

We multiply all the terms by the denominator


x*12x-5*12x+7=0

Wy multiply elements

12x^2-60x+7=0

a = 12; b = -60; c = +7;
Δ = b2-4ac
Δ = -602-4·12·7
Δ = 3264
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:

$\sqrt{\Delta}=\sqrt{3264}=\sqrt{64*51}=\sqrt{64}*\sqrt{51}=8\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-8\sqrt{51}}{2*12}=\frac{60-8\sqrt{51}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+8\sqrt{51}}{2*12}=\frac{60+8\sqrt{51}}{24}
$