(2x+1)(6-x)=21

Solution for (2x+1)(6-x)=21 equation:

(2x+1)(6-x)=21

We move all terms to the left:

(2x+1)(6-x)-(21)=0

We add all the numbers together, and all the variables

(2x+1)(-1x+6)-21=0

We multiply parentheses ..

(-2x^2+12x-1x+6)-21=0

We get rid of parentheses

-2x^2+12x-1x+6-21=0

We add all the numbers together, and all the variables

-2x^2+11x-15=0

a = -2; b = 11; c = -15;
Δ = b2-4ac
Δ = 112-4·(-2)·(-15)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-1}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+1}{2*-2}=\frac{-10}{-4}
=2+1/2
$