225x^2+1=30

Solution for 225x^2+1=30 equation:

225x^2+1=30

We move all terms to the left:

225x^2+1-(30)=0

We add all the numbers together, and all the variables

225x^2-29=0

a = 225; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·225·(-29)
Δ = 26100
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:

$\sqrt{\Delta}=\sqrt{26100}=\sqrt{900*29}=\sqrt{900}*\sqrt{29}=30\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{29}}{2*225}=\frac{0-30\sqrt{29}}{450}
=-\frac{30\sqrt{29}}{450}
=-\frac{\sqrt{29}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{29}}{2*225}=\frac{0+30\sqrt{29}}{450}
=\frac{30\sqrt{29}}{450}
=\frac{\sqrt{29}}{15}
$