7a+5(a+3)=8a+4(a+2)7a+5(a+3)=8a+4(a+2)

Solution for 7a+5(a+3)=8a+4(a+2)7a+5(a+3)=8a+4(a+2) equation:

7a+5(a+3)=8a+4(a+2)7a+5(a+3)=8a+4(a+2)

We move all terms to the left:

7a+5(a+3)-(8a+4(a+2)7a+5(a+3))=0

We multiply parentheses

7a+5a-(8a+4(a+2)7a+5(a+3))+15=0


We calculate terms in parentheses: -(8a+4(a+2)7a+5(a+3)), so:

8a+4(a+2)7a+5(a+3)

We multiply parentheses

28a^2+8a+56a+5a+15

We add all the numbers together, and all the variables

28a^2+69a+15

Back to the equation:

-(28a^2+69a+15)


We add all the numbers together, and all the variables

12a-(28a^2+69a+15)+15=0

We get rid of parentheses

-28a^2+12a-69a-15+15=0

We add all the numbers together, and all the variables

-28a^2-57a=0

a = -28; b = -57; c = 0;
Δ = b2-4ac
Δ = -572-4·(-28)·0
Δ = 3249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3249}=57$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-57}{2*-28}=\frac{0}{-56}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+57}{2*-28}=\frac{114}{-56}
=-2+1/28
$