11.5x2=23

Solution for 11.5x2=23 equation:

11.5x^2=23

We move all terms to the left:

11.5x^2-(23)=0

a = 11.5; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·11.5·(-23)
Δ = 1058
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:

$\sqrt{\Delta}=\sqrt{1058}=\sqrt{529*2}=\sqrt{529}*\sqrt{2}=23\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-23\sqrt{2}}{2*11.5}=\frac{0-23\sqrt{2}}{23}
=-\frac{23\sqrt{2}}{23}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+23\sqrt{2}}{2*11.5}=\frac{0+23\sqrt{2}}{23}
=\frac{23\sqrt{2}}{23}
=\sqrt{2}
$