9x^2-4x+7=12

Solution for 9x^2-4x+7=12 equation:

9x^2-4x+7=12

We move all terms to the left:

9x^2-4x+7-(12)=0

We add all the numbers together, and all the variables

9x^2-4x-5=0

a = 9; b = -4; c = -5;
Δ = b2-4ac
Δ = -42-4·9·(-5)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-14}{2*9}=\frac{-10}{18}
=-5/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+14}{2*9}=\frac{18}{18}
=1
$