9x2=2+7x

Solution for 9x2=2+7x equation:

9x^2=2+7x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

9x^2-7x-2=0

a = 9; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·9·(-2)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-11}{2*9}=\frac{-4}{18}
=-2/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*9}=\frac{18}{18}
=1
$