60-2,1/4x=2+5x

Solution for 60-2,1/4x=2+5x equation:

60-2.1/4x=2+5x

We move all terms to the left:

60-2.1/4x-(2+5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-2.1/4x-(5x+2)+60=0

We get rid of parentheses

-2.1/4x-5x-2+60=0

We multiply all the terms by the denominator


-5x*4x-2*4x+60*4x-2.1=0

Wy multiply elements

-20x^2-8x+240x-2.1=0

We add all the numbers together, and all the variables

-20x^2+232x-2.1=0

a = -20; b = 232; c = -2.1;
Δ = b2-4ac
Δ = 2322-4·(-20)·(-2.1)
Δ = 53656
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:

$\sqrt{\Delta}=\sqrt{53656}=\sqrt{4*13414}=\sqrt{4}*\sqrt{13414}=2\sqrt{13414}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(232)-2\sqrt{13414}}{2*-20}=\frac{-232-2\sqrt{13414}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(232)+2\sqrt{13414}}{2*-20}=\frac{-232+2\sqrt{13414}}{-40}
$