3/4x-5=4x=

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

3/4x-5=4x=

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply all the terms by the denominator


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

Wy multiply elements

-16x^2-20x+3=0

a = -16; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·(-16)·3
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{37}}{2*-16}=\frac{20-4\sqrt{37}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{37}}{2*-16}=\frac{20+4\sqrt{37}}{-32}
$