3(x+13)-15=4x(x-2)-9

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Solution for 3(x+13)-15=4x(x-2)-9 equation:



3(x+13)-15=4x(x-2)-9
We move all terms to the left:
3(x+13)-15-(4x(x-2)-9)=0
We multiply parentheses
3x-(4x(x-2)-9)+39-15=0
We calculate terms in parentheses: -(4x(x-2)-9), so:
4x(x-2)-9
We multiply parentheses
4x^2-8x-9
Back to the equation:
-(4x^2-8x-9)
We add all the numbers together, and all the variables
3x-(4x^2-8x-9)+24=0
We get rid of parentheses
-4x^2+3x+8x+9+24=0
We add all the numbers together, and all the variables
-4x^2+11x+33=0
a = -4; b = 11; c = +33;
Δ = b2-4ac
Δ = 112-4·(-4)·33
Δ = 649
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{-(11)-\sqrt{649}}{2*-4}=\frac{-11-\sqrt{649}}{-8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{649}}{2*-4}=\frac{-11+\sqrt{649}}{-8} $

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