7x^2-2x+9=16

Solution for 7x^2-2x+9=16 equation:

7x^2-2x+9=16

We move all terms to the left:

7x^2-2x+9-(16)=0

We add all the numbers together, and all the variables

7x^2-2x-7=0

a = 7; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·7·(-7)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10\sqrt{2}}{2*7}=\frac{2-10\sqrt{2}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10\sqrt{2}}{2*7}=\frac{2+10\sqrt{2}}{14}
$