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

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

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

We move all terms to the left:

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

We multiply parentheses ..

-((+2x^2-7x+6x-21))+x=0


We calculate terms in parentheses: -((+2x^2-7x+6x-21)), so:

(+2x^2-7x+6x-21)

We get rid of parentheses

2x^2-7x+6x-21

We add all the numbers together, and all the variables

2x^2-1x-21

Back to the equation:

-(2x^2-1x-21)


We add all the numbers together, and all the variables

x-(2x^2-1x-21)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2x^2+2x+21=0

a = -2; b = 2; c = +21;
Δ = b2-4ac
Δ = 22-4·(-2)·21
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{43}}{2*-2}=\frac{-2-2\sqrt{43}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{43}}{2*-2}=\frac{-2+2\sqrt{43}}{-4}
$