-3/4x-7=2x+3

Solution for -3/4x-7=2x+3 equation:

-3/4x-7=2x+3

We move all terms to the left:

-3/4x-7-(2x+3)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

-3/4x-2x-3-7=0

We multiply all the terms by the denominator


-2x*4x-3*4x-7*4x-3=0

Wy multiply elements

-8x^2-12x-28x-3=0

We add all the numbers together, and all the variables

-8x^2-40x-3=0

a = -8; b = -40; c = -3;
Δ = b2-4ac
Δ = -402-4·(-8)·(-3)
Δ = 1504
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:

$\sqrt{\Delta}=\sqrt{1504}=\sqrt{16*94}=\sqrt{16}*\sqrt{94}=4\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{94}}{2*-8}=\frac{40-4\sqrt{94}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{94}}{2*-8}=\frac{40+4\sqrt{94}}{-16}
$