3/4x=4x-5

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

3/4x=4x-5

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-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}
$