10x^2+3=102

Solution for 10x^2+3=102 equation:

10x^2+3=102

We move all terms to the left:

10x^2+3-(102)=0

We add all the numbers together, and all the variables

10x^2-99=0

a = 10; b = 0; c = -99;
Δ = b2-4ac
Δ = 02-4·10·(-99)
Δ = 3960
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:

$\sqrt{\Delta}=\sqrt{3960}=\sqrt{36*110}=\sqrt{36}*\sqrt{110}=6\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{110}}{2*10}=\frac{0-6\sqrt{110}}{20}
=-\frac{6\sqrt{110}}{20}
=-\frac{3\sqrt{110}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{110}}{2*10}=\frac{0+6\sqrt{110}}{20}
=\frac{6\sqrt{110}}{20}
=\frac{3\sqrt{110}}{10}
$