(5/2x^2-2)(2x)=115

Solution for (5/2x^2-2)(2x)=115 equation:

(5/2x^2-2)(2x)=115

We move all terms to the left:

(5/2x^2-2)(2x)-(115)=0


Domain of the equation: 2x^2-2)2x!=0

x∈R


We multiply parentheses

10x^2-4x-115=0

a = 10; b = -4; c = -115;
Δ = b2-4ac
Δ = -42-4·10·(-115)
Δ = 4616
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:

$\sqrt{\Delta}=\sqrt{4616}=\sqrt{4*1154}=\sqrt{4}*\sqrt{1154}=2\sqrt{1154}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{1154}}{2*10}=\frac{4-2\sqrt{1154}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{1154}}{2*10}=\frac{4+2\sqrt{1154}}{20}
$