5/8x+4x=3/8x+12

Solution for 5/8x+4x=3/8x+12 equation:

5/8x+4x=3/8x+12

We move all terms to the left:

5/8x+4x-(3/8x+12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 8x+12)!=0

x∈R


We add all the numbers together, and all the variables

4x+5/8x-(3/8x+12)=0

We get rid of parentheses

4x+5/8x-3/8x-12=0

We multiply all the terms by the denominator


4x*8x-12*8x+5-3=0

We add all the numbers together, and all the variables

4x*8x-12*8x+2=0

Wy multiply elements

32x^2-96x+2=0

a = 32; b = -96; c = +2;
Δ = b2-4ac
Δ = -962-4·32·2
Δ = 8960
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:

$\sqrt{\Delta}=\sqrt{8960}=\sqrt{256*35}=\sqrt{256}*\sqrt{35}=16\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-16\sqrt{35}}{2*32}=\frac{96-16\sqrt{35}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+16\sqrt{35}}{2*32}=\frac{96+16\sqrt{35}}{64}
$