(x+2)(x-9)=(7x+17)

Solution for (x+2)(x-9)=(7x+17) equation:

(x+2)(x-9)=(7x+17)

We move all terms to the left:

(x+2)(x-9)-((7x+17))=0

We multiply parentheses ..

(+x^2-9x+2x-18)-((7x+17))=0


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

(7x+17)

We get rid of parentheses

7x+17

Back to the equation:

-(7x+17)


We get rid of parentheses

x^2-9x+2x-7x-18-17=0

We add all the numbers together, and all the variables

x^2-14x-35=0

a = 1; b = -14; c = -35;
Δ = b2-4ac
Δ = -142-4·1·(-35)
Δ = 336
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:

$\sqrt{\Delta}=\sqrt{336}=\sqrt{16*21}=\sqrt{16}*\sqrt{21}=4\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{21}}{2*1}=\frac{14-4\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{21}}{2*1}=\frac{14+4\sqrt{21}}{2}
$