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(2x+5)(3x+2)=(9x-1)(5x-4)

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Solution for (2x+5)(3x+2)=(9x-1)(5x-4) equation:



(2x+5)(3x+2)=(9x-1)(5x-4)
We move all terms to the left:
(2x+5)(3x+2)-((9x-1)(5x-4))=0
We multiply parentheses ..
(+6x^2+4x+15x+10)-((9x-1)(5x-4))=0
We calculate terms in parentheses: -((9x-1)(5x-4)), so:
(9x-1)(5x-4)
We multiply parentheses ..
(+45x^2-36x-5x+4)
We get rid of parentheses
45x^2-36x-5x+4
We add all the numbers together, and all the variables
45x^2-41x+4
Back to the equation:
-(45x^2-41x+4)
We get rid of parentheses
6x^2-45x^2+4x+15x+41x+10-4=0
We add all the numbers together, and all the variables
-39x^2+60x+6=0
a = -39; b = 60; c = +6;
Δ = b2-4ac
Δ = 602-4·(-39)·6
Δ = 4536
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{4536}=\sqrt{324*14}=\sqrt{324}*\sqrt{14}=18\sqrt{14}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-18\sqrt{14}}{2*-39}=\frac{-60-18\sqrt{14}}{-78}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+18\sqrt{14}}{2*-39}=\frac{-60+18\sqrt{14}}{-78}

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