3x^2+100x+35000=242900

Solution for 3x^2+100x+35000=242900 equation:

3x^2+100x+35000=242900

We move all terms to the left:

3x^2+100x+35000-(242900)=0

We add all the numbers together, and all the variables

3x^2+100x-207900=0

a = 3; b = 100; c = -207900;
Δ = b2-4ac
Δ = 1002-4·3·(-207900)
Δ = 2504800
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:

$\sqrt{\Delta}=\sqrt{2504800}=\sqrt{400*6262}=\sqrt{400}*\sqrt{6262}=20\sqrt{6262}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{6262}}{2*3}=\frac{-100-20\sqrt{6262}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{6262}}{2*3}=\frac{-100+20\sqrt{6262}}{6}
$