3x^2+5=103

Solution for 3x^2+5=103 equation:

3x^2+5=103

We move all terms to the left:

3x^2+5-(103)=0

We add all the numbers together, and all the variables

3x^2-98=0

a = 3; b = 0; c = -98;
Δ = b2-4ac
Δ = 02-4·3·(-98)
Δ = 1176
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:

$\sqrt{\Delta}=\sqrt{1176}=\sqrt{196*6}=\sqrt{196}*\sqrt{6}=14\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{6}}{2*3}=\frac{0-14\sqrt{6}}{6}
=-\frac{14\sqrt{6}}{6}
=-\frac{7\sqrt{6}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{6}}{2*3}=\frac{0+14\sqrt{6}}{6}
=\frac{14\sqrt{6}}{6}
=\frac{7\sqrt{6}}{3}
$