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(3x+19)(5x-29)=360
We move all terms to the left:
(3x+19)(5x-29)-(360)=0
We multiply parentheses ..
(+15x^2-87x+95x-551)-360=0
We get rid of parentheses
15x^2-87x+95x-551-360=0
We add all the numbers together, and all the variables
15x^2+8x-911=0
a = 15; b = 8; c = -911;
Δ = b2-4ac
Δ = 82-4·15·(-911)
Δ = 54724
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{54724}=\sqrt{4*13681}=\sqrt{4}*\sqrt{13681}=2\sqrt{13681}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{13681}}{2*15}=\frac{-8-2\sqrt{13681}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{13681}}{2*15}=\frac{-8+2\sqrt{13681}}{30} $
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