3x+4=7-x(x+17)

Solution for 3x+4=7-x(x+17) equation:

3x+4=7-x(x+17)

We move all terms to the left:

3x+4-(7-x(x+17))=0


We calculate terms in parentheses: -(7-x(x+17)), so:

7-x(x+17)

determiningTheFunctionDomain
-x(x+17)+7

We multiply parentheses

-x^2-17x+7

We add all the numbers together, and all the variables

-1x^2-17x+7

Back to the equation:

-(-1x^2-17x+7)


We get rid of parentheses

1x^2+17x+3x-7+4=0

We add all the numbers together, and all the variables

x^2+20x-3=0

a = 1; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·1·(-3)
Δ = 412
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:

$\sqrt{\Delta}=\sqrt{412}=\sqrt{4*103}=\sqrt{4}*\sqrt{103}=2\sqrt{103}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{103}}{2*1}=\frac{-20-2\sqrt{103}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{103}}{2*1}=\frac{-20+2\sqrt{103}}{2}
$