4x+3x2=102

Solution for 4x+3x2=102 equation:

4x+3x^2=102

We move all terms to the left:

4x+3x^2-(102)=0

a = 3; b = 4; c = -102;
Δ = b2-4ac
Δ = 42-4·3·(-102)
Δ = 1240
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:

$\sqrt{\Delta}=\sqrt{1240}=\sqrt{4*310}=\sqrt{4}*\sqrt{310}=2\sqrt{310}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{310}}{2*3}=\frac{-4-2\sqrt{310}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{310}}{2*3}=\frac{-4+2\sqrt{310}}{6}
$