24x-7x^2=9

Solution for 24x-7x^2=9 equation:

24x-7x^2=9

We move all terms to the left:

24x-7x^2-(9)=0

a = -7; b = 24; c = -9;
Δ = b2-4ac
Δ = 242-4·(-7)·(-9)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-18}{2*-7}=\frac{-42}{-14}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+18}{2*-7}=\frac{-6}{-14}
=3/7
$