5y^2-5y-715/4=100

Solution for 5y^2-5y-715/4=100 equation:

5y^2-5y-715/4=100

We move all terms to the left:

5y^2-5y-715/4-(100)=0

determiningTheFunctionDomain
5y^2-5y-100-715/4=0

We multiply all the terms by the denominator


5y^2*4-5y*4-715-100*4=0

We add all the numbers together, and all the variables

5y^2*4-5y*4-1115=0

Wy multiply elements

20y^2-20y-1115=0

a = 20; b = -20; c = -1115;
Δ = b2-4ac
Δ = -202-4·20·(-1115)
Δ = 89600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{89600}=\sqrt{6400*14}=\sqrt{6400}*\sqrt{14}=80\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-80\sqrt{14}}{2*20}=\frac{20-80\sqrt{14}}{40}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+80\sqrt{14}}{2*20}=\frac{20+80\sqrt{14}}{40}
$