(15x-2)(7x+4)=x

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Solution for (15x-2)(7x+4)=x equation:



(15x-2)(7x+4)=x
We move all terms to the left:
(15x-2)(7x+4)-(x)=0
We add all the numbers together, and all the variables
-1x+(15x-2)(7x+4)=0
We multiply parentheses ..
(+105x^2+60x-14x-8)-1x=0
We get rid of parentheses
105x^2+60x-14x-1x-8=0
We add all the numbers together, and all the variables
105x^2+45x-8=0
a = 105; b = 45; c = -8;
Δ = b2-4ac
Δ = 452-4·105·(-8)
Δ = 5385
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-\sqrt{5385}}{2*105}=\frac{-45-\sqrt{5385}}{210} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{5385}}{2*105}=\frac{-45+\sqrt{5385}}{210} $

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