921x^2+115=174

Solution for 921x^2+115=174 equation:

921x^2+115=174

We move all terms to the left:

921x^2+115-(174)=0

We add all the numbers together, and all the variables

921x^2-59=0

a = 921; b = 0; c = -59;
Δ = b2-4ac
Δ = 02-4·921·(-59)
Δ = 217356
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:

$\sqrt{\Delta}=\sqrt{217356}=\sqrt{4*54339}=\sqrt{4}*\sqrt{54339}=2\sqrt{54339}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{54339}}{2*921}=\frac{0-2\sqrt{54339}}{1842}
=-\frac{2\sqrt{54339}}{1842}
=-\frac{\sqrt{54339}}{921}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{54339}}{2*921}=\frac{0+2\sqrt{54339}}{1842}
=\frac{2\sqrt{54339}}{1842}
=\frac{\sqrt{54339}}{921}
$