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7h(11-h)=-5
We move all terms to the left:
7h(11-h)-(-5)=0
We add all the numbers together, and all the variables
7h(-1h+11)-(-5)=0
We add all the numbers together, and all the variables
7h(-1h+11)+5=0
We multiply parentheses
-7h^2+77h+5=0
a = -7; b = 77; c = +5;
Δ = b2-4ac
Δ = 772-4·(-7)·5
Δ = 6069
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}$$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6069}=\sqrt{289*21}=\sqrt{289}*\sqrt{21}=17\sqrt{21}$$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(77)-17\sqrt{21}}{2*-7}=\frac{-77-17\sqrt{21}}{-14} $$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(77)+17\sqrt{21}}{2*-7}=\frac{-77+17\sqrt{21}}{-14} $
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