(3x+2)(2x-7)=140

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Solution for (3x+2)(2x-7)=140 equation:



(3x+2)(2x-7)=140
We move all terms to the left:
(3x+2)(2x-7)-(140)=0
We multiply parentheses ..
(+6x^2-21x+4x-14)-140=0
We get rid of parentheses
6x^2-21x+4x-14-140=0
We add all the numbers together, and all the variables
6x^2-17x-154=0
a = 6; b = -17; c = -154;
Δ = b2-4ac
Δ = -172-4·6·(-154)
Δ = 3985
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{-(-17)-\sqrt{3985}}{2*6}=\frac{17-\sqrt{3985}}{12} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{3985}}{2*6}=\frac{17+\sqrt{3985}}{12} $

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