78-x=1/3x+46

Solution for 78-x=1/3x+46 equation:

78-x=1/3x+46

We move all terms to the left:

78-x-(1/3x+46)=0


Domain of the equation: 3x+46)!=0

x∈R


We add all the numbers together, and all the variables

-1x-(1/3x+46)+78=0

We get rid of parentheses

-1x-1/3x-46+78=0

We multiply all the terms by the denominator


-1x*3x-46*3x+78*3x-1=0

Wy multiply elements

-3x^2-138x+234x-1=0

We add all the numbers together, and all the variables

-3x^2+96x-1=0

a = -3; b = 96; c = -1;
Δ = b2-4ac
Δ = 962-4·(-3)·(-1)
Δ = 9204
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:

$\sqrt{\Delta}=\sqrt{9204}=\sqrt{4*2301}=\sqrt{4}*\sqrt{2301}=2\sqrt{2301}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-2\sqrt{2301}}{2*-3}=\frac{-96-2\sqrt{2301}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+2\sqrt{2301}}{2*-3}=\frac{-96+2\sqrt{2301}}{-6}
$