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(3x-5)(x+3)=60

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Solution for (3x-5)(x+3)=60 equation:



(3x-5)(x+3)=60
We move all terms to the left:
(3x-5)(x+3)-(60)=0
We multiply parentheses ..
(+3x^2+9x-5x-15)-60=0
We get rid of parentheses
3x^2+9x-5x-15-60=0
We add all the numbers together, and all the variables
3x^2+4x-75=0
a = 3; b = 4; c = -75;
Δ = b2-4ac
Δ = 42-4·3·(-75)
Δ = 916
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{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{229}}{2*3}=\frac{-4-2\sqrt{229}}{6}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{229}}{2*3}=\frac{-4+2\sqrt{229}}{6}

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