4*49-c^2=55

Solution for 4*49-c^2=55 equation:

4*49-c^2=55

We move all terms to the left:

4*49-c^2-(55)=0

determiningTheFunctionDomain
-c^2-55+4*49=0

We add all the numbers together, and all the variables

-1c^2+141=0

a = -1; b = 0; c = +141;
Δ = b2-4ac
Δ = 02-4·(-1)·141
Δ = 564
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{564}=\sqrt{4*141}=\sqrt{4}*\sqrt{141}=2\sqrt{141}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{141}}{2*-1}=\frac{0-2\sqrt{141}}{-2}
=-\frac{2\sqrt{141}}{-2}
=-\frac{\sqrt{141}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{141}}{2*-1}=\frac{0+2\sqrt{141}}{-2}
=\frac{2\sqrt{141}}{-2}
=\frac{\sqrt{141}}{-1}
$