X+21=(3x+8)(2x+1)

Solution for X+21=(3x+8)(2x+1) equation:

X+21=(3X+8)(2X+1)

We move all terms to the left:

X+21-((3X+8)(2X+1))=0

We multiply parentheses ..

-((+6X^2+3X+16X+8))+X+21=0


We calculate terms in parentheses: -((+6X^2+3X+16X+8)), so:

(+6X^2+3X+16X+8)

We get rid of parentheses

6X^2+3X+16X+8

We add all the numbers together, and all the variables

6X^2+19X+8

Back to the equation:

-(6X^2+19X+8)


We add all the numbers together, and all the variables

X-(6X^2+19X+8)+21=0

We get rid of parentheses

-6X^2+X-19X-8+21=0

We add all the numbers together, and all the variables

-6X^2-18X+13=0

a = -6; b = -18; c = +13;
Δ = b2-4ac
Δ = -182-4·(-6)·13
Δ = 636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{636}=\sqrt{4*159}=\sqrt{4}*\sqrt{159}=2\sqrt{159}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{159}}{2*-6}=\frac{18-2\sqrt{159}}{-12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{159}}{2*-6}=\frac{18+2\sqrt{159}}{-12}
$