8x^2+6,28x^2-100=0

Solution for 8x^2+6,28x^2-100=0 equation:

8x^2+6.28x^2-100=0

We add all the numbers together, and all the variables

14.28x^2-100=0

a = 14.28; b = 0; c = -100;
Δ = b2-4ac
Δ = 02-4·14.28·(-100)
Δ = 5712
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:

$\sqrt{\Delta}=\sqrt{5712}=\sqrt{16*357}=\sqrt{16}*\sqrt{357}=4\sqrt{357}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{357}}{2*14.28}=\frac{0-4\sqrt{357}}{28.56}
=-\frac{4\sqrt{357}}{28.56}
=-\frac{\sqrt{357}}{7.14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{357}}{2*14.28}=\frac{0+4\sqrt{357}}{28.56}
=\frac{4\sqrt{357}}{28.56}
=\frac{\sqrt{357}}{7.14}
$