34-7x^2=-218

Solution for 34-7x^2=-218 equation:

34-7x^2=-218

We move all terms to the left:

34-7x^2-(-218)=0

We add all the numbers together, and all the variables

-7x^2+252=0

a = -7; b = 0; c = +252;
Δ = b2-4ac
Δ = 02-4·(-7)·252
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-84}{2*-7}=\frac{-84}{-14}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+84}{2*-7}=\frac{84}{-14}
=-6
$