3x^2+100x+35000=260000

Solution for 3x^2+100x+35000=260000 equation:

3x^2+100x+35000=260000

We move all terms to the left:

3x^2+100x+35000-(260000)=0

We add all the numbers together, and all the variables

3x^2+100x-225000=0

a = 3; b = 100; c = -225000;
Δ = b2-4ac
Δ = 1002-4·3·(-225000)
Δ = 2710000
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:

$\sqrt{\Delta}=\sqrt{2710000}=\sqrt{10000*271}=\sqrt{10000}*\sqrt{271}=100\sqrt{271}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-100\sqrt{271}}{2*3}=\frac{-100-100\sqrt{271}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+100\sqrt{271}}{2*3}=\frac{-100+100\sqrt{271}}{6}
$