x-(-3/4x-9)=-5

Solution for x-(-3/4x-9)=-5 equation:

x-(-3/4x-9)=-5

We move all terms to the left:

x-(-3/4x-9)-(-5)=0


Domain of the equation: 4x-9)!=0

x∈R


We add all the numbers together, and all the variables

x-(-3/4x-9)+5=0

We get rid of parentheses

x+3/4x+9+5=0

We multiply all the terms by the denominator


x*4x+9*4x+5*4x+3=0

Wy multiply elements

4x^2+36x+20x+3=0

We add all the numbers together, and all the variables

4x^2+56x+3=0

a = 4; b = 56; c = +3;
Δ = b2-4ac
Δ = 562-4·4·3
Δ = 3088
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:

$\sqrt{\Delta}=\sqrt{3088}=\sqrt{16*193}=\sqrt{16}*\sqrt{193}=4\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-4\sqrt{193}}{2*4}=\frac{-56-4\sqrt{193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+4\sqrt{193}}{2*4}=\frac{-56+4\sqrt{193}}{8}
$