x(x+1)-195/4=0

Solution for x(x+1)-195/4=0 equation:

x(x+1)-195/4=0

We multiply parentheses

x^2+x-195/4=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+4x-195=0

a = 4; b = 4; c = -195;
Δ = b2-4ac
Δ = 42-4·4·(-195)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-56}{2*4}=\frac{-60}{8}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+56}{2*4}=\frac{52}{8}
=6+1/2
$