3.8x+4=5/2x-4

Solution for 3.8x+4=5/2x-4 equation:

3.8x+4=5/2x-4

We move all terms to the left:

3.8x+4-(5/2x-4)=0


Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

3.8x-5/2x+4+4=0

We multiply all the terms by the denominator


(3.8x)*2x+4*2x+4*2x-5=0

We add all the numbers together, and all the variables

(+3.8x)*2x+4*2x+4*2x-5=0

We multiply parentheses

6x^2+4*2x+4*2x-5=0

Wy multiply elements

6x^2+8x+8x-5=0

We add all the numbers together, and all the variables

6x^2+16x-5=0

a = 6; b = 16; c = -5;
Δ = b2-4ac
Δ = 162-4·6·(-5)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{94}}{2*6}=\frac{-16-2\sqrt{94}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{94}}{2*6}=\frac{-16+2\sqrt{94}}{12}
$