5+3x*x=82

Solution for 5+3x*x=82 equation:

5+3x*x=82

We move all terms to the left:

5+3x*x-(82)=0

We add all the numbers together, and all the variables

3x*x-77=0

Wy multiply elements

3x^2-77=0

a = 3; b = 0; c = -77;
Δ = b2-4ac
Δ = 02-4·3·(-77)
Δ = 924
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:

$\sqrt{\Delta}=\sqrt{924}=\sqrt{4*231}=\sqrt{4}*\sqrt{231}=2\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{231}}{2*3}=\frac{0-2\sqrt{231}}{6}
=-\frac{2\sqrt{231}}{6}
=-\frac{\sqrt{231}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{231}}{2*3}=\frac{0+2\sqrt{231}}{6}
=\frac{2\sqrt{231}}{6}
=\frac{\sqrt{231}}{3}
$