3x*x-9x-7=5x-7

Solution for 3x*x-9x-7=5x-7 equation:

3x*x-9x-7=5x-7

We move all terms to the left:

3x*x-9x-7-(5x-7)=0

We add all the numbers together, and all the variables

-9x+3x*x-(5x-7)-7=0

Wy multiply elements

3x^2-9x-(5x-7)-7=0

We get rid of parentheses

3x^2-9x-5x+7-7=0

We add all the numbers together, and all the variables

3x^2-14x=0

a = 3; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·3·0
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*3}=\frac{0}{6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*3}=\frac{28}{6}
=4+2/3
$