4x(2x+4)=10x+15-2x+1

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Solution for 4x(2x+4)=10x+15-2x+1 equation:



4x(2x+4)=10x+15-2x+1
We move all terms to the left:
4x(2x+4)-(10x+15-2x+1)=0
We add all the numbers together, and all the variables
4x(2x+4)-(8x+16)=0
We multiply parentheses
8x^2+16x-(8x+16)=0
We get rid of parentheses
8x^2+16x-8x-16=0
We add all the numbers together, and all the variables
8x^2+8x-16=0
a = 8; b = 8; c = -16;
Δ = b2-4ac
Δ = 82-4·8·(-16)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-24}{2*8}=\frac{-32}{16} =-2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+24}{2*8}=\frac{16}{16} =1 $

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