1/4x+2=-5.8x-5

Solution for 1/4x+2=-5.8x-5 equation:

1/4x+2=-5.8x-5

We move all terms to the left:

1/4x+2-(-5.8x-5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x+5.8x+5+2=0

We multiply all the terms by the denominator


(5.8x)*4x+5*4x+2*4x+1=0

We add all the numbers together, and all the variables

(+5.8x)*4x+5*4x+2*4x+1=0

We multiply parentheses

20x^2+5*4x+2*4x+1=0

Wy multiply elements

20x^2+20x+8x+1=0

We add all the numbers together, and all the variables

20x^2+28x+1=0

a = 20; b = 28; c = +1;
Δ = b2-4ac
Δ = 282-4·20·1
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-8\sqrt{11}}{2*20}=\frac{-28-8\sqrt{11}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+8\sqrt{11}}{2*20}=\frac{-28+8\sqrt{11}}{40}
$