6x=(2x+3)(3x-7)

Solution for 6x=(2x+3)(3x-7) equation:

6x=(2x+3)(3x-7)

We move all terms to the left:

6x-((2x+3)(3x-7))=0

We multiply parentheses ..

-((+6x^2-14x+9x-21))+6x=0


We calculate terms in parentheses: -((+6x^2-14x+9x-21)), so:

(+6x^2-14x+9x-21)

We get rid of parentheses

6x^2-14x+9x-21

We add all the numbers together, and all the variables

6x^2-5x-21

Back to the equation:

-(6x^2-5x-21)


We add all the numbers together, and all the variables

6x-(6x^2-5x-21)=0

We get rid of parentheses

-6x^2+6x+5x+21=0

We add all the numbers together, and all the variables

-6x^2+11x+21=0

a = -6; b = 11; c = +21;
Δ = b2-4ac
Δ = 112-4·(-6)·21
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-25}{2*-6}=\frac{-36}{-12}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+25}{2*-6}=\frac{14}{-12}
=-1+1/6
$