1/2(h+6)(h-6)=140

Solution for 1/2(h+6)(h-6)=140 equation:

1/2(h+6)(h-6)=140

We move all terms to the left:

1/2(h+6)(h-6)-(140)=0


Domain of the equation: 2(h+6)(h-6)!=0

h∈R


We use the square of the difference formula

h^2-36-140=0

We add all the numbers together, and all the variables

h^2-176=0

a = 1; b = 0; c = -176;
Δ = b2-4ac
Δ = 02-4·1·(-176)
Δ = 704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{704}=\sqrt{64*11}=\sqrt{64}*\sqrt{11}=8\sqrt{11}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{11}}{2*1}=\frac{0-8\sqrt{11}}{2}
=-\frac{8\sqrt{11}}{2}
=-4\sqrt{11}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{11}}{2*1}=\frac{0+8\sqrt{11}}{2}
=\frac{8\sqrt{11}}{2}
=4\sqrt{11}
$