3x^2+4x^2=1000

Solution for 3x^2+4x^2=1000 equation:

3x^2+4x^2=1000

We move all terms to the left:

3x^2+4x^2-(1000)=0

We add all the numbers together, and all the variables

7x^2-1000=0

a = 7; b = 0; c = -1000;
Δ = b2-4ac
Δ = 02-4·7·(-1000)
Δ = 28000
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:

$\sqrt{\Delta}=\sqrt{28000}=\sqrt{400*70}=\sqrt{400}*\sqrt{70}=20\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{70}}{2*7}=\frac{0-20\sqrt{70}}{14}
=-\frac{20\sqrt{70}}{14}
=-\frac{10\sqrt{70}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{70}}{2*7}=\frac{0+20\sqrt{70}}{14}
=\frac{20\sqrt{70}}{14}
=\frac{10\sqrt{70}}{7}
$