3x^2+x-2=1200

Solution for 3x^2+x-2=1200 equation:

3x^2+x-2=1200

We move all terms to the left:

3x^2+x-2-(1200)=0

We add all the numbers together, and all the variables

3x^2+x-1202=0

a = 3; b = 1; c = -1202;
Δ = b2-4ac
Δ = 12-4·3·(-1202)
Δ = 14425
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:

$\sqrt{\Delta}=\sqrt{14425}=\sqrt{25*577}=\sqrt{25}*\sqrt{577}=5\sqrt{577}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{577}}{2*3}=\frac{-1-5\sqrt{577}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{577}}{2*3}=\frac{-1+5\sqrt{577}}{6}
$