1/4x+6=5x-51

Solution for 1/4x+6=5x-51 equation:

1/4x+6=5x-51

We move all terms to the left:

1/4x+6-(5x-51)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-5x+51+6=0

We multiply all the terms by the denominator


-5x*4x+51*4x+6*4x+1=0

Wy multiply elements

-20x^2+204x+24x+1=0

We add all the numbers together, and all the variables

-20x^2+228x+1=0

a = -20; b = 228; c = +1;
Δ = b2-4ac
Δ = 2282-4·(-20)·1
Δ = 52064
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:

$\sqrt{\Delta}=\sqrt{52064}=\sqrt{16*3254}=\sqrt{16}*\sqrt{3254}=4\sqrt{3254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(228)-4\sqrt{3254}}{2*-20}=\frac{-228-4\sqrt{3254}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(228)+4\sqrt{3254}}{2*-20}=\frac{-228+4\sqrt{3254}}{-40}
$