(a+1)(a-3)+(2a-3)(5-7a=)

Solution for (a+1)(a-3)+(2a-3)(5-7a=) equation:

(a+1)(a-3)+(2a-3)(5-7a=)

We move all terms to the left:

(a+1)(a-3)+(2a-3)(5-7a-())=0

We multiply parentheses ..

(+a^2-3a+a-3)+(2a-3)(5-7a-())=0


We calculate terms in parentheses: +(2a-3)(5-7a-()), so:

2a-3)(5-7a-()

determiningTheFunctionDomain
2a-7a-3)(5-()

We add all the numbers together, and all the variables

-5a

Back to the equation:

+(-5a)


We get rid of parentheses

a^2-3a+a-5a-3=0

We add all the numbers together, and all the variables

a^2-7a-3=0

a = 1; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·1·(-3)
Δ = 61
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{61}}{2*1}=\frac{7-\sqrt{61}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{61}}{2*1}=\frac{7+\sqrt{61}}{2}
$