3(x-5)(2x+3)=21

Solution for 3(x-5)(2x+3)=21 equation:

3(x-5)(2x+3)=21

We move all terms to the left:

3(x-5)(2x+3)-(21)=0

We multiply parentheses ..

3(+2x^2+3x-10x-15)-21=0

We multiply parentheses

6x^2+9x-30x-45-21=0

We add all the numbers together, and all the variables

6x^2-21x-66=0

a = 6; b = -21; c = -66;
Δ = b2-4ac
Δ = -212-4·6·(-66)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-45}{2*6}=\frac{-24}{12}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+45}{2*6}=\frac{66}{12}
=5+1/2
$