(a+3)(0+7)=a(a+3)-7

Solution for (a+3)(0+7)=a(a+3)-7 equation:

(a+3)(0+7)=a(a+3)-7

We move all terms to the left:

(a+3)(0+7)-(a(a+3)-7)=0

We add all the numbers together, and all the variables

(a+3)7-(a(a+3)-7)=0

We multiply parentheses

7a-(a(a+3)-7)+21=0


We calculate terms in parentheses: -(a(a+3)-7), so:

a(a+3)-7

We multiply parentheses

a^2+3a-7

Back to the equation:

-(a^2+3a-7)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1a^2+4a+28=0

a = -1; b = 4; c = +28;
Δ = b2-4ac
Δ = 42-4·(-1)·28
Δ = 128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{128}=\sqrt{64*2}=\sqrt{64}*\sqrt{2}=8\sqrt{2}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{2}}{2*-1}=\frac{-4-8\sqrt{2}}{-2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{2}}{2*-1}=\frac{-4+8\sqrt{2}}{-2}
$