5(x-6)-9=4+3/4x

Solution for 5(x-6)-9=4+3/4x equation:

5(x-6)-9=4+3/4x

We move all terms to the left:

5(x-6)-9-(4+3/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5(x-6)-(3/4x+4)-9=0

We multiply parentheses

5x-(3/4x+4)-30-9=0

We get rid of parentheses

5x-3/4x-4-30-9=0

We multiply all the terms by the denominator


5x*4x-4*4x-30*4x-9*4x-3=0

Wy multiply elements

20x^2-16x-120x-36x-3=0

We add all the numbers together, and all the variables

20x^2-172x-3=0

a = 20; b = -172; c = -3;
Δ = b2-4ac
Δ = -1722-4·20·(-3)
Δ = 29824
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:

$\sqrt{\Delta}=\sqrt{29824}=\sqrt{64*466}=\sqrt{64}*\sqrt{466}=8\sqrt{466}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-172)-8\sqrt{466}}{2*20}=\frac{172-8\sqrt{466}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-172)+8\sqrt{466}}{2*20}=\frac{172+8\sqrt{466}}{40}
$