7+3x=3/4x+1

Solution for 7+3x=3/4x+1 equation:

7+3x=3/4x+1

We move all terms to the left:

7+3x-(3/4x+1)=0


Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

3x-3/4x-1+7=0

We multiply all the terms by the denominator


3x*4x-1*4x+7*4x-3=0

Wy multiply elements

12x^2-4x+28x-3=0

We add all the numbers together, and all the variables

12x^2+24x-3=0

a = 12; b = 24; c = -3;
Δ = b2-4ac
Δ = 242-4·12·(-3)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-12\sqrt{5}}{2*12}=\frac{-24-12\sqrt{5}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+12\sqrt{5}}{2*12}=\frac{-24+12\sqrt{5}}{24}
$