13x^2+9=45

Solution for 13x^2+9=45 equation:

13x^2+9=45

We move all terms to the left:

13x^2+9-(45)=0

We add all the numbers together, and all the variables

13x^2-36=0

a = 13; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·13·(-36)
Δ = 1872
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:

$\sqrt{\Delta}=\sqrt{1872}=\sqrt{144*13}=\sqrt{144}*\sqrt{13}=12\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{13}}{2*13}=\frac{0-12\sqrt{13}}{26}
=-\frac{12\sqrt{13}}{26}
=-\frac{6\sqrt{13}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{13}}{2*13}=\frac{0+12\sqrt{13}}{26}
=\frac{12\sqrt{13}}{26}
=\frac{6\sqrt{13}}{13}
$