-3.8x-1/2x=-56

Solution for -3.8x-1/2x=-56 equation:

-3.8x-1/2x=-56

We move all terms to the left:

-3.8x-1/2x-(-56)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-3.8x-1/2x+56=0

We multiply all the terms by the denominator


-(3.8x)*2x+56*2x-1=0

We add all the numbers together, and all the variables

-(+3.8x)*2x+56*2x-1=0

We multiply parentheses

-6x^2+56*2x-1=0

Wy multiply elements

-6x^2+112x-1=0

a = -6; b = 112; c = -1;
Δ = b2-4ac
Δ = 1122-4·(-6)·(-1)
Δ = 12520
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:

$\sqrt{\Delta}=\sqrt{12520}=\sqrt{4*3130}=\sqrt{4}*\sqrt{3130}=2\sqrt{3130}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-2\sqrt{3130}}{2*-6}=\frac{-112-2\sqrt{3130}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+2\sqrt{3130}}{2*-6}=\frac{-112+2\sqrt{3130}}{-12}
$