5+6x=4-3x(-18x-3)

Solution for 5+6x=4-3x(-18x-3) equation:

5+6x=4-3x(-18x-3)

We move all terms to the left:

5+6x-(4-3x(-18x-3))=0


We calculate terms in parentheses: -(4-3x(-18x-3)), so:

4-3x(-18x-3)

determiningTheFunctionDomain
-3x(-18x-3)+4

We multiply parentheses

54x^2+9x+4

Back to the equation:

-(54x^2+9x+4)


We get rid of parentheses

-54x^2+6x-9x-4+5=0

We add all the numbers together, and all the variables

-54x^2-3x+1=0

a = -54; b = -3; c = +1;
Δ = b2-4ac
Δ = -32-4·(-54)·1
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*-54}=\frac{-12}{-108}
=1/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*-54}=\frac{18}{-108}
=-1/6
$