(9x-26)(2x-12)=4x+43

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Solution for (9x-26)(2x-12)=4x+43 equation:



(9x-26)(2x-12)=4x+43
We move all terms to the left:
(9x-26)(2x-12)-(4x+43)=0
We get rid of parentheses
(9x-26)(2x-12)-4x-43=0
We multiply parentheses ..
(+18x^2-108x-52x+312)-4x-43=0
We get rid of parentheses
18x^2-108x-52x-4x+312-43=0
We add all the numbers together, and all the variables
18x^2-164x+269=0
a = 18; b = -164; c = +269;
Δ = b2-4ac
Δ = -1642-4·18·269
Δ = 7528
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:
$\sqrt{\Delta}=\sqrt{7528}=\sqrt{4*1882}=\sqrt{4}*\sqrt{1882}=2\sqrt{1882}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-164)-2\sqrt{1882}}{2*18}=\frac{164-2\sqrt{1882}}{36} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-164)+2\sqrt{1882}}{2*18}=\frac{164+2\sqrt{1882}}{36} $

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