7x^2=7x+9

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

7x^2=7x+9

We move all terms to the left:

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

We get rid of parentheses

7x^2-7x-9=0

a = 7; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·7·(-9)
Δ = 301
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{301}}{2*7}=\frac{7-\sqrt{301}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{301}}{2*7}=\frac{7+\sqrt{301}}{14}
$