4x^2+10=342

Solution for 4x^2+10=342 equation:

4x^2+10=342

We move all terms to the left:

4x^2+10-(342)=0

We add all the numbers together, and all the variables

4x^2-332=0

a = 4; b = 0; c = -332;
Δ = b2-4ac
Δ = 02-4·4·(-332)
Δ = 5312
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:

$\sqrt{\Delta}=\sqrt{5312}=\sqrt{64*83}=\sqrt{64}*\sqrt{83}=8\sqrt{83}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{83}}{2*4}=\frac{0-8\sqrt{83}}{8}
=-\frac{8\sqrt{83}}{8}
=-\sqrt{83}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{83}}{2*4}=\frac{0+8\sqrt{83}}{8}
=\frac{8\sqrt{83}}{8}
=\sqrt{83}
$