9x^2-14x=x^2

Solution for 9x^2-14x=x^2 equation:

9x^2-14x=x^2

We move all terms to the left:

9x^2-14x-(x^2)=0

determiningTheFunctionDomain
9x^2-x^2-14x=0

We add all the numbers together, and all the variables

8x^2-14x=0

a = 8; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·8·0
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{-(-14)-14}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*8}=\frac{28}{16}
=1+3/4
$