36x+9x+5=(2x+3)(3x+2)

Solution for 36x+9x+5=(2x+3)(3x+2) equation:

36x+9x+5=(2x+3)(3x+2)

We move all terms to the left:

36x+9x+5-((2x+3)(3x+2))=0

We add all the numbers together, and all the variables

45x-((2x+3)(3x+2))+5=0

We multiply parentheses ..

-((+6x^2+4x+9x+6))+45x+5=0


We calculate terms in parentheses: -((+6x^2+4x+9x+6)), so:

(+6x^2+4x+9x+6)

We get rid of parentheses

6x^2+4x+9x+6

We add all the numbers together, and all the variables

6x^2+13x+6

Back to the equation:

-(6x^2+13x+6)


We add all the numbers together, and all the variables

45x-(6x^2+13x+6)+5=0

We get rid of parentheses

-6x^2+45x-13x-6+5=0

We add all the numbers together, and all the variables

-6x^2+32x-1=0

a = -6; b = 32; c = -1;
Δ = b2-4ac
Δ = 322-4·(-6)·(-1)
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-10\sqrt{10}}{2*-6}=\frac{-32-10\sqrt{10}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+10\sqrt{10}}{2*-6}=\frac{-32+10\sqrt{10}}{-12}
$