3-7x^2=-557

Solution for 3-7x^2=-557 equation:

3-7x^2=-557

We move all terms to the left:

3-7x^2-(-557)=0

We add all the numbers together, and all the variables

-7x^2+560=0

a = -7; b = 0; c = +560;
Δ = b2-4ac
Δ = 02-4·(-7)·560
Δ = 15680
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:

$\sqrt{\Delta}=\sqrt{15680}=\sqrt{3136*5}=\sqrt{3136}*\sqrt{5}=56\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-56\sqrt{5}}{2*-7}=\frac{0-56\sqrt{5}}{-14}
=-\frac{56\sqrt{5}}{-14}
=-\frac{4\sqrt{5}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+56\sqrt{5}}{2*-7}=\frac{0+56\sqrt{5}}{-14}
=\frac{56\sqrt{5}}{-14}
=\frac{4\sqrt{5}}{-1}
$