5/8x+4=3.8x+12

Solution for 5/8x+4=3.8x+12 equation:

5/8x+4=3.8x+12

We move all terms to the left:

5/8x+4-(3.8x+12)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

5/8x-3.8x-12+4=0

We multiply all the terms by the denominator


-(3.8x)*8x-12*8x+4*8x+5=0

We add all the numbers together, and all the variables

-(+3.8x)*8x-12*8x+4*8x+5=0

We multiply parentheses

-24x^2-12*8x+4*8x+5=0

Wy multiply elements

-24x^2-96x+32x+5=0

We add all the numbers together, and all the variables

-24x^2-64x+5=0

a = -24; b = -64; c = +5;
Δ = b2-4ac
Δ = -642-4·(-24)·5
Δ = 4576
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:

$\sqrt{\Delta}=\sqrt{4576}=\sqrt{16*286}=\sqrt{16}*\sqrt{286}=4\sqrt{286}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{286}}{2*-24}=\frac{64-4\sqrt{286}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{286}}{2*-24}=\frac{64+4\sqrt{286}}{-48}
$