315*x^2+315*x-1=0

Solution for 315*x^2+315*x-1=0 equation:

315x^2+315*x-1=0

We add all the numbers together, and all the variables

315x^2+315x-1=0

a = 315; b = 315; c = -1;
Δ = b2-4ac
Δ = 3152-4·315·(-1)
Δ = 100485
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:

$\sqrt{\Delta}=\sqrt{100485}=\sqrt{9*11165}=\sqrt{9}*\sqrt{11165}=3\sqrt{11165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(315)-3\sqrt{11165}}{2*315}=\frac{-315-3\sqrt{11165}}{630}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(315)+3\sqrt{11165}}{2*315}=\frac{-315+3\sqrt{11165}}{630}
$