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2+7/4x+5=2x-1/4x
We move all terms to the left:
2+7/4x+5-(2x-1/4x)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
7/4x-(+2x-1/4x)+2+5=0
We add all the numbers together, and all the variables
7/4x-(+2x-1/4x)+7=0
We get rid of parentheses
7/4x-2x+1/4x+7=0
We multiply all the terms by the denominator
-2x*4x+7*4x+7+1=0
We add all the numbers together, and all the variables
-2x*4x+7*4x+8=0
Wy multiply elements
-8x^2+28x+8=0
a = -8; b = 28; c = +8;
Δ = b2-4ac
Δ = 282-4·(-8)·8
Δ = 1040
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{65}}{2*-8}=\frac{-28-4\sqrt{65}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{65}}{2*-8}=\frac{-28+4\sqrt{65}}{-16} $
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