5z^2+14z+196/9=223/9

Solution for 5z^2+14z+196/9=223/9 equation:

5z^2+14z+196/9=223/9

We move all terms to the left:

5z^2+14z+196/9-(223/9)=0

We add all the numbers together, and all the variables

5z^2+14z+196/9-(+223/9)=0

We get rid of parentheses

5z^2+14z+196/9-223/9=0

We multiply all the terms by the denominator


5z^2*9+14z*9+196-223=0

We add all the numbers together, and all the variables

5z^2*9+14z*9-27=0

Wy multiply elements

45z^2+126z-27=0

a = 45; b = 126; c = -27;
Δ = b2-4ac
Δ = 1262-4·45·(-27)
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(126)-144}{2*45}=\frac{-270}{90}
=-3
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(126)+144}{2*45}=\frac{18}{90}
=1/5
$