(X-7)(x+3)=(x+2)+5

Solution for (X-7)(x+3)=(x+2)+5 equation:

(X-7)(X+3)=(X+2)+5

We move all terms to the left:

(X-7)(X+3)-((X+2)+5)=0

We multiply parentheses ..

(+X^2+3X-7X-21)-((X+2)+5)=0


We calculate terms in parentheses: -((X+2)+5), so:

(X+2)+5

We get rid of parentheses

X+2+5

We add all the numbers together, and all the variables

X+7

Back to the equation:

-(X+7)


We get rid of parentheses

X^2+3X-7X-X-21-7=0

We add all the numbers together, and all the variables

X^2-5X-28=0

a = 1; b = -5; c = -28;
Δ = b2-4ac
Δ = -52-4·1·(-28)
Δ = 137
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{137}}{2*1}=\frac{5-\sqrt{137}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{137}}{2*1}=\frac{5+\sqrt{137}}{2}
$