X=(x+7)(2x+3)

Solution for X=(x+7)(2x+3) equation:

X=(X+7)(2X+3)

We move all terms to the left:

X-((X+7)(2X+3))=0

We multiply parentheses ..

-((+2X^2+3X+14X+21))+X=0


We calculate terms in parentheses: -((+2X^2+3X+14X+21)), so:

(+2X^2+3X+14X+21)

We get rid of parentheses

2X^2+3X+14X+21

We add all the numbers together, and all the variables

2X^2+17X+21

Back to the equation:

-(2X^2+17X+21)


We add all the numbers together, and all the variables

X-(2X^2+17X+21)=0

We get rid of parentheses

-2X^2+X-17X-21=0

We add all the numbers together, and all the variables

-2X^2-16X-21=0

a = -2; b = -16; c = -21;
Δ = b2-4ac
Δ = -162-4·(-2)·(-21)
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{22}}{2*-2}=\frac{16-2\sqrt{22}}{-4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{22}}{2*-2}=\frac{16+2\sqrt{22}}{-4}
$