4x2+14=47.75

Solution for 4x2+14=47.75 equation:

4x^2+14=47.75

We move all terms to the left:

4x^2+14-(47.75)=0

We add all the numbers together, and all the variables

4x^2-33.75=0

a = 4; b = 0; c = -33.75;
Δ = b2-4ac
Δ = 02-4·4·(-33.75)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{15}}{2*4}=\frac{0-6\sqrt{15}}{8}
=-\frac{6\sqrt{15}}{8}
=-\frac{3\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{15}}{2*4}=\frac{0+6\sqrt{15}}{8}
=\frac{6\sqrt{15}}{8}
=\frac{3\sqrt{15}}{4}
$