7y^2+15y-2y^2=25+y^2

Solution for 7y^2+15y-2y^2=25+y^2 equation:

7y^2+15y-2y^2=25+y^2

We move all terms to the left:

7y^2+15y-2y^2-(25+y^2)=0

We add all the numbers together, and all the variables

5y^2-(25+y^2)+15y=0

We get rid of parentheses

5y^2-y^2+15y-25=0

We add all the numbers together, and all the variables

4y^2+15y-25=0

a = 4; b = 15; c = -25;
Δ = b2-4ac
Δ = 152-4·4·(-25)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-25}{2*4}=\frac{-40}{8}
=-5
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+25}{2*4}=\frac{10}{8}
=1+1/4
$