5a(a+2)=4(a+1)

Solution for 5a(a+2)=4(a+1) equation:

5a(a+2)=4(a+1)

We move all terms to the left:

5a(a+2)-(4(a+1))=0

We multiply parentheses

5a^2+10a-(4(a+1))=0


We calculate terms in parentheses: -(4(a+1)), so:

4(a+1)

We multiply parentheses

4a+4

Back to the equation:

-(4a+4)


We get rid of parentheses

5a^2+10a-4a-4=0

We add all the numbers together, and all the variables

5a^2+6a-4=0

a = 5; b = 6; c = -4;
Δ = b2-4ac
Δ = 62-4·5·(-4)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{29}}{2*5}=\frac{-6-2\sqrt{29}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{29}}{2*5}=\frac{-6+2\sqrt{29}}{10}
$