3(2x-5)(3x+4)=0

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Solution for 3(2x-5)(3x+4)=0 equation:



3(2x-5)(3x+4)=0
We multiply parentheses ..
3(+6x^2+8x-15x-20)=0
We multiply parentheses
18x^2+24x-45x-60=0
We add all the numbers together, and all the variables
18x^2-21x-60=0
a = 18; b = -21; c = -60;
Δ = b2-4ac
Δ = -212-4·18·(-60)
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-69}{2*18}=\frac{-48}{36} =-1+1/3 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+69}{2*18}=\frac{90}{36} =2+1/2 $

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