48a+20a^2=2

Solution for 48a+20a^2=2 equation:

48a+20a^2=2

We move all terms to the left:

48a+20a^2-(2)=0

a = 20; b = 48; c = -2;
Δ = b2-4ac
Δ = 482-4·20·(-2)
Δ = 2464
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:

$\sqrt{\Delta}=\sqrt{2464}=\sqrt{16*154}=\sqrt{16}*\sqrt{154}=4\sqrt{154}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-4\sqrt{154}}{2*20}=\frac{-48-4\sqrt{154}}{40}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+4\sqrt{154}}{2*20}=\frac{-48+4\sqrt{154}}{40}
$