3x^2=245x-2000

Solution for 3x^2=245x-2000 equation:

3x^2=245x-2000

We move all terms to the left:

3x^2-(245x-2000)=0

We get rid of parentheses

3x^2-245x+2000=0

a = 3; b = -245; c = +2000;
Δ = b2-4ac
Δ = -2452-4·3·2000
Δ = 36025
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:

$\sqrt{\Delta}=\sqrt{36025}=\sqrt{25*1441}=\sqrt{25}*\sqrt{1441}=5\sqrt{1441}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-245)-5\sqrt{1441}}{2*3}=\frac{245-5\sqrt{1441}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-245)+5\sqrt{1441}}{2*3}=\frac{245+5\sqrt{1441}}{6}
$