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(3/4)(h+2)=15
We move all terms to the left:
(3/4)(h+2)-(15)=0
Domain of the equation: 4)(h+2)!=0We add all the numbers together, and all the variables
h∈R
(+3/4)(h+2)-15=0
We multiply parentheses ..
(+3h^2+3/4*2)-15=0
We multiply all the terms by the denominator
(+3h^2+3-15*4*2)=0
We get rid of parentheses
3h^2+3-15*4*2=0
We add all the numbers together, and all the variables
3h^2-117=0
a = 3; b = 0; c = -117;
Δ = b2-4ac
Δ = 02-4·3·(-117)
Δ = 1404
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}$$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{39}}{2*3}=\frac{0-6\sqrt{39}}{6} =-\frac{6\sqrt{39}}{6} =-\sqrt{39} $$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{39}}{2*3}=\frac{0+6\sqrt{39}}{6} =\frac{6\sqrt{39}}{6} =\sqrt{39} $
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