30x-10=5x^2-1

Solution for 30x-10=5x^2-1 equation:

30x-10=5x^2-1

We move all terms to the left:

30x-10-(5x^2-1)=0

We get rid of parentheses

-5x^2+30x+1-10=0

We add all the numbers together, and all the variables

-5x^2+30x-9=0

a = -5; b = 30; c = -9;
Δ = b2-4ac
Δ = 302-4·(-5)·(-9)
Δ = 720
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-12\sqrt{5}}{2*-5}=\frac{-30-12\sqrt{5}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+12\sqrt{5}}{2*-5}=\frac{-30+12\sqrt{5}}{-10}
$