49-7x2=14

Solution for 49-7x2=14 equation:

49-7x^2=14

We move all terms to the left:

49-7x^2-(14)=0

We add all the numbers together, and all the variables

-7x^2+35=0

a = -7; b = 0; c = +35;
Δ = b2-4ac
Δ = 02-4·(-7)·35
Δ = 980
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:

$\sqrt{\Delta}=\sqrt{980}=\sqrt{196*5}=\sqrt{196}*\sqrt{5}=14\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{5}}{2*-7}=\frac{0-14\sqrt{5}}{-14}
=-\frac{14\sqrt{5}}{-14}
=-\frac{\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{5}}{2*-7}=\frac{0+14\sqrt{5}}{-14}
=\frac{14\sqrt{5}}{-14}
=\frac{\sqrt{5}}{-1}
$