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

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

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

We move all terms to the left:

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

We multiply parentheses

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


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

8a+4(a+2)

We multiply parentheses

8a+4a+8

We add all the numbers together, and all the variables

12a+8

Back to the equation:

-(12a+8)


We add all the numbers together, and all the variables

5a^2+22a-(12a+8)=0

We get rid of parentheses

5a^2+22a-12a-8=0

We add all the numbers together, and all the variables

5a^2+10a-8=0

a = 5; b = 10; c = -8;
Δ = b2-4ac
Δ = 102-4·5·(-8)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{65}}{2*5}=\frac{-10-2\sqrt{65}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{65}}{2*5}=\frac{-10+2\sqrt{65}}{10}
$