5x(2x-3)=3(4x+7)

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Solution for 5x(2x-3)=3(4x+7) equation:



5x(2x-3)=3(4x+7)
We move all terms to the left:
5x(2x-3)-(3(4x+7))=0
We multiply parentheses
10x^2-15x-(3(4x+7))=0
We calculate terms in parentheses: -(3(4x+7)), so:
3(4x+7)
We multiply parentheses
12x+21
Back to the equation:
-(12x+21)
We get rid of parentheses
10x^2-15x-12x-21=0
We add all the numbers together, and all the variables
10x^2-27x-21=0
a = 10; b = -27; c = -21;
Δ = b2-4ac
Δ = -272-4·10·(-21)
Δ = 1569
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{-(-27)-\sqrt{1569}}{2*10}=\frac{27-\sqrt{1569}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+\sqrt{1569}}{2*10}=\frac{27+\sqrt{1569}}{20} $

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