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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+x^2-2x+7x-14)-((2x+2))=0


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

(2x+2)

We get rid of parentheses

2x+2

Back to the equation:

-(2x+2)


We get rid of parentheses

x^2-2x+7x-2x-14-2=0

We add all the numbers together, and all the variables

x^2+3x-16=0

a = 1; b = 3; c = -16;
Δ = b2-4ac
Δ = 32-4·1·(-16)
Δ = 73
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{-(3)-\sqrt{73}}{2*1}=\frac{-3-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{73}}{2*1}=\frac{-3+\sqrt{73}}{2}
$