3x2+4x=127

Solution for 3x2+4x=127 equation:

3x^2+4x=127

We move all terms to the left:

3x^2+4x-(127)=0

a = 3; b = 4; c = -127;
Δ = b2-4ac
Δ = 42-4·3·(-127)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{385}}{2*3}=\frac{-4-2\sqrt{385}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{385}}{2*3}=\frac{-4+2\sqrt{385}}{6}
$