19x2-23=183

Solution for 19x2-23=183 equation:

19x^2-23=183

We move all terms to the left:

19x^2-23-(183)=0

We add all the numbers together, and all the variables

19x^2-206=0

a = 19; b = 0; c = -206;
Δ = b2-4ac
Δ = 02-4·19·(-206)
Δ = 15656
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:

$\sqrt{\Delta}=\sqrt{15656}=\sqrt{4*3914}=\sqrt{4}*\sqrt{3914}=2\sqrt{3914}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3914}}{2*19}=\frac{0-2\sqrt{3914}}{38}
=-\frac{2\sqrt{3914}}{38}
=-\frac{\sqrt{3914}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3914}}{2*19}=\frac{0+2\sqrt{3914}}{38}
=\frac{2\sqrt{3914}}{38}
=\frac{\sqrt{3914}}{19}
$