19x^2-15=33

Solution for 19x^2-15=33 equation:

19x^2-15=33

We move all terms to the left:

19x^2-15-(33)=0

We add all the numbers together, and all the variables

19x^2-48=0

a = 19; b = 0; c = -48;
Δ = b2-4ac
Δ = 02-4·19·(-48)
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{57}}{2*19}=\frac{0-8\sqrt{57}}{38}
=-\frac{8\sqrt{57}}{38}
=-\frac{4\sqrt{57}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{57}}{2*19}=\frac{0+8\sqrt{57}}{38}
=\frac{8\sqrt{57}}{38}
=\frac{4\sqrt{57}}{19}
$