9x-7x2=5x-6

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-7x^2+4x+6=0

a = -7; b = 4; c = +6;
Δ = b2-4ac
Δ = 42-4·(-7)·6
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{46}}{2*-7}=\frac{-4-2\sqrt{46}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{46}}{2*-7}=\frac{-4+2\sqrt{46}}{-14}
$