1/3x+10-4x=32

Solution for 1/3x+10-4x=32 equation:

1/3x+10-4x=32

We move all terms to the left:

1/3x+10-4x-(32)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+1/3x-22=0

We multiply all the terms by the denominator


-4x*3x-22*3x+1=0

Wy multiply elements

-12x^2-66x+1=0

a = -12; b = -66; c = +1;
Δ = b2-4ac
Δ = -662-4·(-12)·1
Δ = 4404
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:

$\sqrt{\Delta}=\sqrt{4404}=\sqrt{4*1101}=\sqrt{4}*\sqrt{1101}=2\sqrt{1101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-2\sqrt{1101}}{2*-12}=\frac{66-2\sqrt{1101}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+2\sqrt{1101}}{2*-12}=\frac{66+2\sqrt{1101}}{-24}
$