y^2+5y-75/4=0

Solution for y^2+5y-75/4=0 equation:

y^2+5y-75/4=0

We multiply all the terms by the denominator


y^2*4+5y*4-75=0

Wy multiply elements

4y^2+20y-75=0

a = 4; b = 20; c = -75;
Δ = b2-4ac
Δ = 202-4·4·(-75)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-40}{2*4}=\frac{-60}{8}
=-7+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+40}{2*4}=\frac{20}{8}
=2+1/2
$