4x^2+6x=127

Solution for 4x^2+6x=127 equation:

4x^2+6x=127

We move all terms to the left:

4x^2+6x-(127)=0

a = 4; b = 6; c = -127;
Δ = b2-4ac
Δ = 62-4·4·(-127)
Δ = 2068
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:

$\sqrt{\Delta}=\sqrt{2068}=\sqrt{4*517}=\sqrt{4}*\sqrt{517}=2\sqrt{517}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{517}}{2*4}=\frac{-6-2\sqrt{517}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{517}}{2*4}=\frac{-6+2\sqrt{517}}{8}
$