y^2-7y=10

Solution for y^2-7y=10 equation:

y^2-7y=10

We move all terms to the left:

y^2-7y-(10)=0

a = 1; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·1·(-10)
Δ = 89
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{-(-7)-\sqrt{89}}{2*1}=\frac{7-\sqrt{89}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{89}}{2*1}=\frac{7+\sqrt{89}}{2}
$