6.28*x^2+3.14*x^2=1000

Solution for 6.28*x^2+3.14*x^2=1000 equation:

6.28x^2+3.14x^2=1000

We move all terms to the left:

6.28x^2+3.14x^2-(1000)=0

We add all the numbers together, and all the variables

9.42x^2-1000=0

a = 9.42; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·9.42·(-1000)
Δ = 37680
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:

$\sqrt{\Delta}=\sqrt{37680}=\sqrt{16*2355}=\sqrt{16}*\sqrt{2355}=4\sqrt{2355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2355}}{2*9.42}=\frac{0-4\sqrt{2355}}{18.84}
=-\frac{4\sqrt{2355}}{18.84}
=-\frac{2\sqrt{2355}}{9.42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2355}}{2*9.42}=\frac{0+4\sqrt{2355}}{18.84}
=\frac{4\sqrt{2355}}{18.84}
=\frac{2\sqrt{2355}}{9.42}
$