19=9+2x(x-7)

Solution for 19=9+2x(x-7) equation:

19=9+2x(x-7)

We move all terms to the left:

19-(9+2x(x-7))=0


We calculate terms in parentheses: -(9+2x(x-7)), so:

9+2x(x-7)

determiningTheFunctionDomain
2x(x-7)+9

We multiply parentheses

2x^2-14x+9

Back to the equation:

-(2x^2-14x+9)


We get rid of parentheses

-2x^2+14x-9+19=0

We add all the numbers together, and all the variables

-2x^2+14x+10=0

a = -2; b = 14; c = +10;
Δ = b2-4ac
Δ = 142-4·(-2)·10
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{69}}{2*-2}=\frac{-14-2\sqrt{69}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{69}}{2*-2}=\frac{-14+2\sqrt{69}}{-4}
$