(8a+6)*(9a+10)=304

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Solution for (8a+6)*(9a+10)=304 equation:



(8a+6)(9a+10)=304
We move all terms to the left:
(8a+6)(9a+10)-(304)=0
We multiply parentheses ..
(+72a^2+80a+54a+60)-304=0
We get rid of parentheses
72a^2+80a+54a+60-304=0
We add all the numbers together, and all the variables
72a^2+134a-244=0
a = 72; b = 134; c = -244;
Δ = b2-4ac
Δ = 1342-4·72·(-244)
Δ = 88228
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{88228}=\sqrt{4*22057}=\sqrt{4}*\sqrt{22057}=2\sqrt{22057}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(134)-2\sqrt{22057}}{2*72}=\frac{-134-2\sqrt{22057}}{144} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(134)+2\sqrt{22057}}{2*72}=\frac{-134+2\sqrt{22057}}{144} $

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