1/5x+27=4x

Solution for 1/5x+27=4x equation:

1/5x+27=4x

We move all terms to the left:

1/5x+27-(4x)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+1/5x+27=0

We multiply all the terms by the denominator


-4x*5x+27*5x+1=0

Wy multiply elements

-20x^2+135x+1=0

a = -20; b = 135; c = +1;
Δ = b2-4ac
Δ = 1352-4·(-20)·1
Δ = 18305
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(135)-\sqrt{18305}}{2*-20}=\frac{-135-\sqrt{18305}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(135)+\sqrt{18305}}{2*-20}=\frac{-135+\sqrt{18305}}{-40}
$