7x-3x2+9=x=4

Solution for 7x-3x2+9=x=4 equation:

7x-3x^2+9=x=4

We move all terms to the left:

7x-3x^2+9-(x)=0

We add all the numbers together, and all the variables

-3x^2+6x+9=0

a = -3; b = 6; c = +9;
Δ = b2-4ac
Δ = 62-4·(-3)·9
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-12}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+12}{2*-3}=\frac{6}{-6}
=-1
$