3x(2x+7)=6(x+4)-3

Solution for 3x(2x+7)=6(x+4)-3 equation:

3x(2x+7)=6(x+4)-3

We move all terms to the left:

3x(2x+7)-(6(x+4)-3)=0

We multiply parentheses

6x^2+21x-(6(x+4)-3)=0


We calculate terms in parentheses: -(6(x+4)-3), so:

6(x+4)-3

We multiply parentheses

6x+24-3

We add all the numbers together, and all the variables

6x+21

Back to the equation:

-(6x+21)


We get rid of parentheses

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

We add all the numbers together, and all the variables

6x^2+15x-21=0

a = 6; b = 15; c = -21;
Δ = b2-4ac
Δ = 152-4·6·(-21)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-27}{2*6}=\frac{-42}{12}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+27}{2*6}=\frac{12}{12}
=1
$