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

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



3+(3)/(2)x+4=4x-(5)/(2)x
We move all terms to the left:
3+(3)/(2)x+4-(4x-(5)/(2)x)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
Domain of the equation: 2x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
3/2x-(+4x-5/2x)+3+4=0
We add all the numbers together, and all the variables
3/2x-(+4x-5/2x)+7=0
We get rid of parentheses
3/2x-4x+5/2x+7=0
We multiply all the terms by the denominator
-4x*2x+7*2x+3+5=0
We add all the numbers together, and all the variables
-4x*2x+7*2x+8=0
Wy multiply elements
-8x^2+14x+8=0
a = -8; b = 14; c = +8;
Δ = b2-4ac
Δ = 142-4·(-8)·8
Δ = 452
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:
$\sqrt{\Delta}=\sqrt{452}=\sqrt{4*113}=\sqrt{4}*\sqrt{113}=2\sqrt{113}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{113}}{2*-8}=\frac{-14-2\sqrt{113}}{-16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{113}}{2*-8}=\frac{-14+2\sqrt{113}}{-16} $

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