4x^2+3^2=1225

Solution for 4x^2+3^2=1225 equation:

4x^2+3^2=1225

We move all terms to the left:

4x^2+3^2-(1225)=0

determiningTheFunctionDomain
4x^2-1225+3^2=0

We add all the numbers together, and all the variables

4x^2-1216=0

a = 4; b = 0; c = -1216;
Δ = b2-4ac
Δ = 02-4·4·(-1216)
Δ = 19456
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:

$\sqrt{\Delta}=\sqrt{19456}=\sqrt{1024*19}=\sqrt{1024}*\sqrt{19}=32\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-32\sqrt{19}}{2*4}=\frac{0-32\sqrt{19}}{8}
=-\frac{32\sqrt{19}}{8}
=-4\sqrt{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+32\sqrt{19}}{2*4}=\frac{0+32\sqrt{19}}{8}
=\frac{32\sqrt{19}}{8}
=4\sqrt{19}
$