3/4x-7=3x+3

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

3/4x-7=3x+3

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-12x^2-40x+3=0

a = -12; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·(-12)·3
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{109}}{2*-12}=\frac{40-4\sqrt{109}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{109}}{2*-12}=\frac{40+4\sqrt{109}}{-24}
$