4x+3x^2=115

Solution for 4x+3x^2=115 equation:

4x+3x^2=115

We move all terms to the left:

4x+3x^2-(115)=0

a = 3; b = 4; c = -115;
Δ = b2-4ac
Δ = 42-4·3·(-115)
Δ = 1396
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:

$\sqrt{\Delta}=\sqrt{1396}=\sqrt{4*349}=\sqrt{4}*\sqrt{349}=2\sqrt{349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{349}}{2*3}=\frac{-4-2\sqrt{349}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{349}}{2*3}=\frac{-4+2\sqrt{349}}{6}
$