10x2+2=292

Solution for 10x2+2=292 equation:

10x^2+2=292

We move all terms to the left:

10x^2+2-(292)=0

We add all the numbers together, and all the variables

10x^2-290=0

a = 10; b = 0; c = -290;
Δ = b2-4ac
Δ = 02-4·10·(-290)
Δ = 11600
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:

$\sqrt{\Delta}=\sqrt{11600}=\sqrt{400*29}=\sqrt{400}*\sqrt{29}=20\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{29}}{2*10}=\frac{0-20\sqrt{29}}{20}
=-\frac{20\sqrt{29}}{20}
=-\sqrt{29}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{29}}{2*10}=\frac{0+20\sqrt{29}}{20}
=\frac{20\sqrt{29}}{20}
=\sqrt{29}
$