7+3/4x=5x

Solution for 7+3/4x=5x equation:

7+3/4x=5x

We move all terms to the left:

7+3/4x-(5x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+3/4x+7=0

We multiply all the terms by the denominator


-5x*4x+7*4x+3=0

Wy multiply elements

-20x^2+28x+3=0

a = -20; b = 28; c = +3;
Δ = b2-4ac
Δ = 282-4·(-20)·3
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-32}{2*-20}=\frac{-60}{-40}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+32}{2*-20}=\frac{4}{-40}
=-1/10
$