y(y-1.5)=52

Solution for y(y-1.5)=52 equation:

y(y-1.5)=52

We move all terms to the left:

y(y-1.5)-(52)=0

We multiply parentheses

y^2-1.5y-52=0

a = 1; b = -1.5; c = -52;
Δ = b2-4ac
Δ = -1.52-4·1·(-52)
Δ = 210.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1.5)-\sqrt{210.25}}{2*1}=\frac{1.5-\sqrt{210.25}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{210.25}}{2*1}=\frac{1.5+\sqrt{210.25}}{2}
$