(7x+4)(3x+9)=(4x+3)(3x+5)

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Solution for (7x+4)(3x+9)=(4x+3)(3x+5) equation:



(7x+4)(3x+9)=(4x+3)(3x+5)
We move all terms to the left:
(7x+4)(3x+9)-((4x+3)(3x+5))=0
We multiply parentheses ..
(+21x^2+63x+12x+36)-((4x+3)(3x+5))=0
We calculate terms in parentheses: -((4x+3)(3x+5)), so:
(4x+3)(3x+5)
We multiply parentheses ..
(+12x^2+20x+9x+15)
We get rid of parentheses
12x^2+20x+9x+15
We add all the numbers together, and all the variables
12x^2+29x+15
Back to the equation:
-(12x^2+29x+15)
We get rid of parentheses
21x^2-12x^2+63x+12x-29x+36-15=0
We add all the numbers together, and all the variables
9x^2+46x+21=0
a = 9; b = 46; c = +21;
Δ = b2-4ac
Δ = 462-4·9·21
Δ = 1360
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:
$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-4\sqrt{85}}{2*9}=\frac{-46-4\sqrt{85}}{18} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+4\sqrt{85}}{2*9}=\frac{-46+4\sqrt{85}}{18} $

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