4z^2+8z^2+10z^2=88^2

Solution for 4z^2+8z^2+10z^2=88^2 equation:

4z^2+8z^2+10z^2=88^2

We move all terms to the left:

4z^2+8z^2+10z^2-(88^2)=0

We add all the numbers together, and all the variables

22z^2-7744=0

a = 22; b = 0; c = -7744;
Δ = b2-4ac
Δ = 02-4·22·(-7744)
Δ = 681472
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{681472}=\sqrt{30976*22}=\sqrt{30976}*\sqrt{22}=176\sqrt{22}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-176\sqrt{22}}{2*22}=\frac{0-176\sqrt{22}}{44}
=-\frac{176\sqrt{22}}{44}
=-4\sqrt{22}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+176\sqrt{22}}{2*22}=\frac{0+176\sqrt{22}}{44}
=\frac{176\sqrt{22}}{44}
=4\sqrt{22}
$