(3x+11)(5x-7)=0

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Solution for (3x+11)(5x-7)=0 equation:



(3x+11)(5x-7)=0
We multiply parentheses ..
(+15x^2-21x+55x-77)=0
We get rid of parentheses
15x^2-21x+55x-77=0
We add all the numbers together, and all the variables
15x^2+34x-77=0
a = 15; b = 34; c = -77;
Δ = b2-4ac
Δ = 342-4·15·(-77)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-76}{2*15}=\frac{-110}{30} =-3+2/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+76}{2*15}=\frac{42}{30} =1+2/5 $

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