3x^2+7x^2=1000

Solution for 3x^2+7x^2=1000 equation:

3x^2+7x^2=1000

We move all terms to the left:

3x^2+7x^2-(1000)=0

We add all the numbers together, and all the variables

10x^2-1000=0

a = 10; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·10·(-1000)
Δ = 40000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{40000}=200$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-200}{2*10}=\frac{-200}{20}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+200}{2*10}=\frac{200}{20}
=10
$