5/12X+7=x

Solution for 5/12X+7=x equation:

5/12X+7=X

We move all terms to the left:

5/12X+7-(X)=0


Domain of the equation: 12X!=0

X!=0/12

X!=0

X∈R


We add all the numbers together, and all the variables

-1X+5/12X+7=0

We multiply all the terms by the denominator


-1X*12X+7*12X+5=0

Wy multiply elements

-12X^2+84X+5=0

a = -12; b = 84; c = +5;
Δ = b2-4ac
Δ = 842-4·(-12)·5
Δ = 7296
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:

$\sqrt{\Delta}=\sqrt{7296}=\sqrt{64*114}=\sqrt{64}*\sqrt{114}=8\sqrt{114}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-8\sqrt{114}}{2*-12}=\frac{-84-8\sqrt{114}}{-24}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+8\sqrt{114}}{2*-12}=\frac{-84+8\sqrt{114}}{-24}
$