(x+7)(x+3)=10(x+2)+2

Solution for (x+7)(x+3)=10(x+2)+2 equation:

(x+7)(x+3)=10(x+2)+2

We move all terms to the left:

(x+7)(x+3)-(10(x+2)+2)=0

We multiply parentheses ..

(+x^2+3x+7x+21)-(10(x+2)+2)=0


We calculate terms in parentheses: -(10(x+2)+2), so:

10(x+2)+2

We multiply parentheses

10x+20+2

We add all the numbers together, and all the variables

10x+22

Back to the equation:

-(10x+22)


We get rid of parentheses

x^2+3x+7x-10x+21-22=0

We add all the numbers together, and all the variables

x^2-1=0

a = 1; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·1·(-1)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2}{2*1}=\frac{-2}{2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2}{2*1}=\frac{2}{2}
=1
$