(5a+2)(2a+1)=10

Solution for (5a+2)(2a+1)=10 equation:

(5a+2)(2a+1)=10

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

10a^2+9a-8=0

a = 10; b = 9; c = -8;
Δ = b2-4ac
Δ = 92-4·10·(-8)
Δ = 401
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{-(9)-\sqrt{401}}{2*10}=\frac{-9-\sqrt{401}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{401}}{2*10}=\frac{-9+\sqrt{401}}{20}
$