27=(2x+3)(x)

Solution for 27=(2x+3)(x) equation:

27=(2x+3)(x)

We move all terms to the left:

27-((2x+3)(x))=0


We calculate terms in parentheses: -((2x+3)x), so:

(2x+3)x

We multiply parentheses

2x^2+3x

Back to the equation:

-(2x^2+3x)


We get rid of parentheses

-2x^2-3x+27=0

a = -2; b = -3; c = +27;
Δ = b2-4ac
Δ = -32-4·(-2)·27
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*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*-2}=\frac{18}{-4}
=-4+1/2
$