4x-7=3+3/4x

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

4x-7=3+3/4x

We move all terms to the left:

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


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2-12x-28x-3=0

We add all the numbers together, and all the variables

16x^2-40x-3=0

a = 16; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·16·(-3)
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-16\sqrt{7}}{2*16}=\frac{40-16\sqrt{7}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+16\sqrt{7}}{2*16}=\frac{40+16\sqrt{7}}{32}
$