4x-1=3/4x+20

Solution for 4x-1=3/4x+20 equation:

4x-1=3/4x+20

We move all terms to the left:

4x-1-(3/4x+20)=0


Domain of the equation: 4x+20)!=0

x∈R


We get rid of parentheses

4x-3/4x-20-1=0

We multiply all the terms by the denominator


4x*4x-20*4x-1*4x-3=0

Wy multiply elements

16x^2-80x-4x-3=0

We add all the numbers together, and all the variables

16x^2-84x-3=0

a = 16; b = -84; c = -3;
Δ = b2-4ac
Δ = -842-4·16·(-3)
Δ = 7248
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:

$\sqrt{\Delta}=\sqrt{7248}=\sqrt{16*453}=\sqrt{16}*\sqrt{453}=4\sqrt{453}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-4\sqrt{453}}{2*16}=\frac{84-4\sqrt{453}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+4\sqrt{453}}{2*16}=\frac{84+4\sqrt{453}}{32}
$