(6x+1)(15x-1)=90

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Solution for (6x+1)(15x-1)=90 equation:



(6x+1)(15x-1)=90
We move all terms to the left:
(6x+1)(15x-1)-(90)=0
We multiply parentheses ..
(+90x^2-6x+15x-1)-90=0
We get rid of parentheses
90x^2-6x+15x-1-90=0
We add all the numbers together, and all the variables
90x^2+9x-91=0
a = 90; b = 9; c = -91;
Δ = b2-4ac
Δ = 92-4·90·(-91)
Δ = 32841
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:
$\sqrt{\Delta}=\sqrt{32841}=\sqrt{9*3649}=\sqrt{9}*\sqrt{3649}=3\sqrt{3649}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{3649}}{2*90}=\frac{-9-3\sqrt{3649}}{180} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{3649}}{2*90}=\frac{-9+3\sqrt{3649}}{180} $

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