3/4x-4=2x+5

Solution for 3/4x-4=2x+5 equation:

3/4x-4=2x+5

We move all terms to the left:

3/4x-4-(2x+5)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

3/4x-2x-5-4=0

We multiply all the terms by the denominator


-2x*4x-5*4x-4*4x+3=0

Wy multiply elements

-8x^2-20x-16x+3=0

We add all the numbers together, and all the variables

-8x^2-36x+3=0

a = -8; b = -36; c = +3;
Δ = b2-4ac
Δ = -362-4·(-8)·3
Δ = 1392
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:

$\sqrt{\Delta}=\sqrt{1392}=\sqrt{16*87}=\sqrt{16}*\sqrt{87}=4\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-4\sqrt{87}}{2*-8}=\frac{36-4\sqrt{87}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+4\sqrt{87}}{2*-8}=\frac{36+4\sqrt{87}}{-16}
$