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(3x+17)(5x+11)=140
We move all terms to the left:
(3x+17)(5x+11)-(140)=0
We multiply parentheses ..
(+15x^2+33x+85x+187)-140=0
We get rid of parentheses
15x^2+33x+85x+187-140=0
We add all the numbers together, and all the variables
15x^2+118x+47=0
a = 15; b = 118; c = +47;
Δ = b2-4ac
Δ = 1182-4·15·47
Δ = 11104
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11104}=\sqrt{16*694}=\sqrt{16}*\sqrt{694}=4\sqrt{694}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(118)-4\sqrt{694}}{2*15}=\frac{-118-4\sqrt{694}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(118)+4\sqrt{694}}{2*15}=\frac{-118+4\sqrt{694}}{30} $
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