48x^2+28x=-3

Solution for 48x^2+28x=-3 equation:

48x^2+28x=-3

We move all terms to the left:

48x^2+28x-(-3)=0

We add all the numbers together, and all the variables

48x^2+28x+3=0

a = 48; b = 28; c = +3;
Δ = b2-4ac
Δ = 282-4·48·3
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{13}}{2*48}=\frac{-28-4\sqrt{13}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{13}}{2*48}=\frac{-28+4\sqrt{13}}{96}
$