How to solve the quadratic equation

Quadratic equation Math Problem
Solve quadratic equation by factorization √(5x² – 6x + 8) – √(5x² – 6x – 7) = 1
Solving the quadratic equation by factorization
Let, u = √(5x² – 6x + 8)
and v = √(5x² – 6x – 7)
then
u – v = 1……….eq(1)
u² – v² = 5x² – 6x + 8 – (5x² – 6x – 7)
⇒ u² – v² = 5x² – 6x + 8 – 5x² + 6x + 7
⇒ u² – v² = 15
we know, u² – v² = (u + v)(u – v)
⇒ 15 = (u + v) × 1
⇒ u + v = 15……….eq(2)
Add equation 1 and equation 2
u – v + u + v = 1 + 15
⇒ 2u = 16
⇒ u = 8
then, v = 7
When u = 8
u² = 64 = 5x² – 6x + 8
⇒ 5x² – 6x – 56 = 0
⇒ 5x² – 20x + 14x – 56 = 0
We can solve the quadratic equation by factorization
so, 5(x – 4) + 14(x – 4) = 0
⇒ (x – 4)(5x + 14) = 0
⇒ x = 4 or x = – 14/5
When u = 7
v² = 49 = 5x² – 6x – 7
⇒ 5x² – 6x – 56 = 0
⇒ x = 4 or x = – 14/5
Now the so the solutions are x = 4 or x = – 14/5