-5x^2=7x-9

Solution for -5x^2=7x-9 equation:

-5x^2=7x-9

We move all terms to the left:

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

We get rid of parentheses

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

a = -5; b = -7; c = +9;
Δ = b2-4ac
Δ = -72-4·(-5)·9
Δ = 229
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{229}}{2*-5}=\frac{7-\sqrt{229}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{229}}{2*-5}=\frac{7+\sqrt{229}}{-10}
$