30a-2=5a^2-5

Solution for 30a-2=5a^2-5 equation:

30a-2=5a^2-5

We move all terms to the left:

30a-2-(5a^2-5)=0

We get rid of parentheses

-5a^2+30a+5-2=0

We add all the numbers together, and all the variables

-5a^2+30a+3=0

a = -5; b = 30; c = +3;
Δ = b2-4ac
Δ = 302-4·(-5)·3
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-8\sqrt{15}}{2*-5}=\frac{-30-8\sqrt{15}}{-10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+8\sqrt{15}}{2*-5}=\frac{-30+8\sqrt{15}}{-10}
$