4x^2+14x=48

Solution for 4x^2+14x=48 equation:

4x^2+14x=48

We move all terms to the left:

4x^2+14x-(48)=0

a = 4; b = 14; c = -48;
Δ = b2-4ac
Δ = 142-4·4·(-48)
Δ = 964
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:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{241}}{2*4}=\frac{-14-2\sqrt{241}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{241}}{2*4}=\frac{-14+2\sqrt{241}}{8}
$