j^2-19j+90.25=64.25

Solution for j^2-19j+90.25=64.25 equation:

j^2-19j+90.25=64.25

We move all terms to the left:

j^2-19j+90.25-(64.25)=0

We add all the numbers together, and all the variables

j^2-19j+26=0

a = 1; b = -19; c = +26;
Δ = b2-4ac
Δ = -192-4·1·26
Δ = 257
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$j_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{257}}{2*1}=\frac{19-\sqrt{257}}{2}
$
$j_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{257}}{2*1}=\frac{19+\sqrt{257}}{2}
$