103(x2)=31

Solution for 103(x2)=31 equation:

103(x2)=31

We move all terms to the left:

103(x2)-(31)=0

We add all the numbers together, and all the variables

103x^2-31=0

a = 103; b = 0; c = -31;
Δ = b2-4ac
Δ = 02-4·103·(-31)
Δ = 12772
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:

$\sqrt{\Delta}=\sqrt{12772}=\sqrt{4*3193}=\sqrt{4}*\sqrt{3193}=2\sqrt{3193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3193}}{2*103}=\frac{0-2\sqrt{3193}}{206}
=-\frac{2\sqrt{3193}}{206}
=-\frac{\sqrt{3193}}{103}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3193}}{2*103}=\frac{0+2\sqrt{3193}}{206}
=\frac{2\sqrt{3193}}{206}
=\frac{\sqrt{3193}}{103}
$