(5x+6)(4x-15)=90

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Solution for (5x+6)(4x-15)=90 equation:



(5x+6)(4x-15)=90
We move all terms to the left:
(5x+6)(4x-15)-(90)=0
We multiply parentheses ..
(+20x^2-75x+24x-90)-90=0
We get rid of parentheses
20x^2-75x+24x-90-90=0
We add all the numbers together, and all the variables
20x^2-51x-180=0
a = 20; b = -51; c = -180;
Δ = b2-4ac
Δ = -512-4·20·(-180)
Δ = 17001
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:
$\sqrt{\Delta}=\sqrt{17001}=\sqrt{9*1889}=\sqrt{9}*\sqrt{1889}=3\sqrt{1889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-3\sqrt{1889}}{2*20}=\frac{51-3\sqrt{1889}}{40} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+3\sqrt{1889}}{2*20}=\frac{51+3\sqrt{1889}}{40} $

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