x(x+2)-195/4=0

Solution for x(x+2)-195/4=0 equation:

x(x+2)-195/4=0

We multiply parentheses

x^2+2x-195/4=0

We multiply all the terms by the denominator


x^2*4+2x*4-195=0

Wy multiply elements

4x^2+8x-195=0

a = 4; b = 8; c = -195;
Δ = b2-4ac
Δ = 82-4·4·(-195)
Δ = 3184
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:

$\sqrt{\Delta}=\sqrt{3184}=\sqrt{16*199}=\sqrt{16}*\sqrt{199}=4\sqrt{199}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{199}}{2*4}=\frac{-8-4\sqrt{199}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{199}}{2*4}=\frac{-8+4\sqrt{199}}{8}
$