(x-7)(x+17)=2^5

Solution for (x-7)(x+17)=2^5 equation:

(x-7)(x+17)=2^5

We move all terms to the left:

(x-7)(x+17)-(2^5)=0

We add all the numbers together, and all the variables

(x-7)(x+17)-32=0

We multiply parentheses ..

(+x^2+17x-7x-119)-32=0

We get rid of parentheses

x^2+17x-7x-119-32=0

We add all the numbers together, and all the variables

x^2+10x-151=0

a = 1; b = 10; c = -151;
Δ = b2-4ac
Δ = 102-4·1·(-151)
Δ = 704
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:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-8\sqrt{11}}{2*1}=\frac{-10-8\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+8\sqrt{11}}{2*1}=\frac{-10+8\sqrt{11}}{2}
$