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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

5a^2+2a-5=0

a = 5; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·5·(-5)
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{26}}{2*5}=\frac{-2-2\sqrt{26}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{26}}{2*5}=\frac{-2+2\sqrt{26}}{10}
$