5=x-17/12x

Solution for 5=x-17/12x equation:

5=x-17/12x

We move all terms to the left:

5-(x-17/12x)=0


Domain of the equation: 12x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+x-17/12x)+5=0

We get rid of parentheses

-x+17/12x+5=0

We multiply all the terms by the denominator


-x*12x+5*12x+17=0

Wy multiply elements

-12x^2+60x+17=0

a = -12; b = 60; c = +17;
Δ = b2-4ac
Δ = 602-4·(-12)·17
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-8\sqrt{69}}{2*-12}=\frac{-60-8\sqrt{69}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+8\sqrt{69}}{2*-12}=\frac{-60+8\sqrt{69}}{-24}
$