12/x+17=45-8x

Solution for 12/x+17=45-8x equation:

12/x+17=45-8x

We move all terms to the left:

12/x+17-(45-8x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

12/x-(-8x+45)+17=0

We get rid of parentheses

12/x+8x-45+17=0

We multiply all the terms by the denominator


8x*x-45*x+17*x+12=0

We add all the numbers together, and all the variables

-28x+8x*x+12=0

Wy multiply elements

8x^2-28x+12=0

a = 8; b = -28; c = +12;
Δ = b2-4ac
Δ = -282-4·8·12
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-20}{2*8}=\frac{8}{16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+20}{2*8}=\frac{48}{16}
=3
$