(X+8)(x-7)=26

Solution for (X+8)(x-7)=26 equation:

(X+8)(X-7)=26

We move all terms to the left:

(X+8)(X-7)-(26)=0

We multiply parentheses ..

(+X^2-7X+8X-56)-26=0

We get rid of parentheses

X^2-7X+8X-56-26=0

We add all the numbers together, and all the variables

X^2+X-82=0

a = 1; b = 1; c = -82;
Δ = b2-4ac
Δ = 12-4·1·(-82)
Δ = 329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{329}}{2*1}=\frac{-1-\sqrt{329}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{329}}{2*1}=\frac{-1+\sqrt{329}}{2}
$