3x+5=9(x+3)6x

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

3x+5=9(x+3)6x

We move all terms to the left:

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


We calculate terms in parentheses: -(9(x+3)6x), so:

9(x+3)6x

We multiply parentheses

54x^2+162x

Back to the equation:

-(54x^2+162x)


We get rid of parentheses

-54x^2+3x-162x+5=0

We add all the numbers together, and all the variables

-54x^2-159x+5=0

a = -54; b = -159; c = +5;
Δ = b2-4ac
Δ = -1592-4·(-54)·5
Δ = 26361
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:

$\sqrt{\Delta}=\sqrt{26361}=\sqrt{9*2929}=\sqrt{9}*\sqrt{2929}=3\sqrt{2929}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-159)-3\sqrt{2929}}{2*-54}=\frac{159-3\sqrt{2929}}{-108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-159)+3\sqrt{2929}}{2*-54}=\frac{159+3\sqrt{2929}}{-108}
$