2y2+y2+5y-16=52

Solution for 2y2+y2+5y-16=52 equation:

2y^2+y2+5y-16=52

We move all terms to the left:

2y^2+y2+5y-16-(52)=0

We add all the numbers together, and all the variables

3y^2+5y-68=0

a = 3; b = 5; c = -68;
Δ = b2-4ac
Δ = 52-4·3·(-68)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-29}{2*3}=\frac{-34}{6}
=-5+2/3
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+29}{2*3}=\frac{24}{6}
=4
$