3x^2+1000=-17x^2+10000

Solution for 3x^2+1000=-17x^2+10000 equation:

3x^2+1000=-17x^2+10000

We move all terms to the left:

3x^2+1000-(-17x^2+10000)=0

We get rid of parentheses

3x^2+17x^2-10000+1000=0

We add all the numbers together, and all the variables

20x^2-9000=0

a = 20; b = 0; c = -9000;
Δ = b2-4ac
Δ = 02-4·20·(-9000)
Δ = 720000
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:

$\sqrt{\Delta}=\sqrt{720000}=\sqrt{360000*2}=\sqrt{360000}*\sqrt{2}=600\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{2}}{2*20}=\frac{0-600\sqrt{2}}{40}
=-\frac{600\sqrt{2}}{40}
=-15\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{2}}{2*20}=\frac{0+600\sqrt{2}}{40}
=\frac{600\sqrt{2}}{40}
=15\sqrt{2}
$