9x^2-35=45

Solution for 9x^2-35=45 equation:

9x^2-35=45

We move all terms to the left:

9x^2-35-(45)=0

We add all the numbers together, and all the variables

9x^2-80=0

a = 9; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·9·(-80)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{5}}{2*9}=\frac{0-24\sqrt{5}}{18}
=-\frac{24\sqrt{5}}{18}
=-\frac{4\sqrt{5}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{5}}{2*9}=\frac{0+24\sqrt{5}}{18}
=\frac{24\sqrt{5}}{18}
=\frac{4\sqrt{5}}{3}
$