(X-2)(x+7)=35

Solution for (X-2)(x+7)=35 equation:

(X-2)(X+7)=35

We move all terms to the left:

(X-2)(X+7)-(35)=0

We multiply parentheses ..

(+X^2+7X-2X-14)-35=0

We get rid of parentheses

X^2+7X-2X-14-35=0

We add all the numbers together, and all the variables

X^2+5X-49=0

a = 1; b = 5; c = -49;
Δ = b2-4ac
Δ = 52-4·1·(-49)
Δ = 221
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{-(5)-\sqrt{221}}{2*1}=\frac{-5-\sqrt{221}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{221}}{2*1}=\frac{-5+\sqrt{221}}{2}
$