8z2+15=22z

Solution for 8z2+15=22z equation:

8z^2+15=22z

We move all terms to the left:

8z^2+15-(22z)=0

a = 8; b = -22; c = +15;
Δ = b2-4ac
Δ = -222-4·8·15
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2}{2*8}=\frac{20}{16}
=1+1/4
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2}{2*8}=\frac{24}{16}
=1+1/2
$