7x-9x2=5x-6

Solution for 7x-9x2=5x-6 equation:

7x-9x^2=5x-6

We move all terms to the left:

7x-9x^2-(5x-6)=0

We get rid of parentheses

-9x^2+7x-5x+6=0

We add all the numbers together, and all the variables

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

a = -9; b = 2; c = +6;
Δ = b2-4ac
Δ = 22-4·(-9)·6
Δ = 220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{220}=\sqrt{4*55}=\sqrt{4}*\sqrt{55}=2\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{55}}{2*-9}=\frac{-2-2\sqrt{55}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{55}}{2*-9}=\frac{-2+2\sqrt{55}}{-18}
$