17-7x2=3

Solution for 17-7x2=3 equation:

17-7x^2=3

We move all terms to the left:

17-7x^2-(3)=0

We add all the numbers together, and all the variables

-7x^2+14=0

a = -7; b = 0; c = +14;
Δ = b2-4ac
Δ = 02-4·(-7)·14
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-14\sqrt{2}}{2*-7}=\frac{0-14\sqrt{2}}{-14}
=-\frac{14\sqrt{2}}{-14}
=-\frac{\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+14\sqrt{2}}{2*-7}=\frac{0+14\sqrt{2}}{-14}
=\frac{14\sqrt{2}}{-14}
=\frac{\sqrt{2}}{-1}
$