1/4x-3=5x-4

Solution for 1/4x-3=5x-4 equation:

1/4x-3=5x-4

We move all terms to the left:

1/4x-3-(5x-4)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

1/4x-5x+4-3=0

We multiply all the terms by the denominator


-5x*4x+4*4x-3*4x+1=0

Wy multiply elements

-20x^2+16x-12x+1=0

We add all the numbers together, and all the variables

-20x^2+4x+1=0

a = -20; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-20)·1
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{6}}{2*-20}=\frac{-4-4\sqrt{6}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{6}}{2*-20}=\frac{-4+4\sqrt{6}}{-40}
$