2x^2+35=1315-3x^-1

Solution for 2x^2+35=1315-3x^-1 equation:

2x^2+35=1315-3x^-1

We move all terms to the left:

2x^2+35-(1315-3x^-1)=0

We get rid of parentheses

2x^2+3x^-1315+1+35=0

We add all the numbers together, and all the variables

2x^2+3x-1279=0

a = 2; b = 3; c = -1279;
Δ = b2-4ac
Δ = 32-4·2·(-1279)
Δ = 10241
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:

$\sqrt{\Delta}=\sqrt{10241}=\sqrt{49*209}=\sqrt{49}*\sqrt{209}=7\sqrt{209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-7\sqrt{209}}{2*2}=\frac{-3-7\sqrt{209}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7\sqrt{209}}{2*2}=\frac{-3+7\sqrt{209}}{4}
$