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

Solution for 0=(6x+7)(x-3) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+6x^2-18x+7x-21))=0


We calculate terms in parentheses: -((+6x^2-18x+7x-21)), so:

(+6x^2-18x+7x-21)

We get rid of parentheses

6x^2-18x+7x-21

We add all the numbers together, and all the variables

6x^2-11x-21

Back to the equation:

-(6x^2-11x-21)


We get rid of parentheses

-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
$