(x+3)(2x-9)=21

Solution for (x+3)(2x-9)=21 equation:

(x+3)(2x-9)=21

We move all terms to the left:

(x+3)(2x-9)-(21)=0

We multiply parentheses ..

(+2x^2-9x+6x-27)-21=0

We get rid of parentheses

2x^2-9x+6x-27-21=0

We add all the numbers together, and all the variables

2x^2-3x-48=0

a = 2; b = -3; c = -48;
Δ = b2-4ac
Δ = -32-4·2·(-48)
Δ = 393
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{393}}{2*2}=\frac{3-\sqrt{393}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{393}}{2*2}=\frac{3+\sqrt{393}}{4}
$