3x^2-x=100

Solution for 3x^2-x=100 equation:

3x^2-x=100

We move all terms to the left:

3x^2-x-(100)=0

We add all the numbers together, and all the variables

3x^2-1x-100=0

a = 3; b = -1; c = -100;
Δ = b2-4ac
Δ = -12-4·3·(-100)
Δ = 1201
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{1201}}{2*3}=\frac{1-\sqrt{1201}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1201}}{2*3}=\frac{1+\sqrt{1201}}{6}
$