4x+3x^2=1200

Solution for 4x+3x^2=1200 equation:

4x+3x^2=1200

We move all terms to the left:

4x+3x^2-(1200)=0

a = 3; b = 4; c = -1200;
Δ = b2-4ac
Δ = 42-4·3·(-1200)
Δ = 14416
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:

$\sqrt{\Delta}=\sqrt{14416}=\sqrt{16*901}=\sqrt{16}*\sqrt{901}=4\sqrt{901}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{901}}{2*3}=\frac{-4-4\sqrt{901}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{901}}{2*3}=\frac{-4+4\sqrt{901}}{6}
$