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

Solution for 3x^2-7x=x^2+9 equation:

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

We move all terms to the left:

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

We get rid of parentheses

3x^2-x^2-7x-9=0

We add all the numbers together, and all the variables

2x^2-7x-9=0

a = 2; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·2·(-9)
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*2}=\frac{-4}{4}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+11}{2*2}=\frac{18}{4}
=4+1/2
$