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(8x+16)(3x+51)=100
We move all terms to the left:
(8x+16)(3x+51)-(100)=0
We multiply parentheses ..
(+24x^2+408x+48x+816)-100=0
We get rid of parentheses
24x^2+408x+48x+816-100=0
We add all the numbers together, and all the variables
24x^2+456x+716=0
a = 24; b = 456; c = +716;
Δ = b2-4ac
Δ = 4562-4·24·716
Δ = 139200
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{139200}=\sqrt{1600*87}=\sqrt{1600}*\sqrt{87}=40\sqrt{87}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(456)-40\sqrt{87}}{2*24}=\frac{-456-40\sqrt{87}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(456)+40\sqrt{87}}{2*24}=\frac{-456+40\sqrt{87}}{48} $
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