25x^2+64=289

Solution for 25x^2+64=289 equation:

25x^2+64=289

We move all terms to the left:

25x^2+64-(289)=0

We add all the numbers together, and all the variables

25x^2-225=0

a = 25; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·25·(-225)
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-150}{2*25}=\frac{-150}{50}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+150}{2*25}=\frac{150}{50}
=3
$