7x^2-7x-206=4

Solution for 7x^2-7x-206=4 equation:

7x^2-7x-206=4

We move all terms to the left:

7x^2-7x-206-(4)=0

We add all the numbers together, and all the variables

7x^2-7x-210=0

a = 7; b = -7; c = -210;
Δ = b2-4ac
Δ = -72-4·7·(-210)
Δ = 5929
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5929}=77$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-77}{2*7}=\frac{-70}{14}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+77}{2*7}=\frac{84}{14}
=6
$