6x^2+9x=(2x+3)

Solution for 6x^2+9x=(2x+3) equation:

6x^2+9x=(2x+3)

We move all terms to the left:

6x^2+9x-((2x+3))=0


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

(2x+3)

We get rid of parentheses

2x+3

Back to the equation:

-(2x+3)


We get rid of parentheses

6x^2+9x-2x-3=0

We add all the numbers together, and all the variables

6x^2+7x-3=0

a = 6; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·6·(-3)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*6}=\frac{4}{12}
=1/3
$