4x-5+(4x2)=47

Solution for 4x-5+(4x2)=47 equation:

4x-5+(4x^2)=47

We move all terms to the left:

4x-5+(4x^2)-(47)=0

determiningTheFunctionDomain
4x^2+4x-5-47=0

We add all the numbers together, and all the variables

4x^2+4x-52=0

a = 4; b = 4; c = -52;
Δ = b2-4ac
Δ = 42-4·4·(-52)
Δ = 848
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:

$\sqrt{\Delta}=\sqrt{848}=\sqrt{16*53}=\sqrt{16}*\sqrt{53}=4\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{53}}{2*4}=\frac{-4-4\sqrt{53}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{53}}{2*4}=\frac{-4+4\sqrt{53}}{8}
$