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1/2x+7=4x+21
We move all terms to the left:
1/2x+7-(4x+21)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
1/2x-4x-21+7=0
We multiply all the terms by the denominator
-4x*2x-21*2x+7*2x+1=0
Wy multiply elements
-8x^2-42x+14x+1=0
We add all the numbers together, and all the variables
-8x^2-28x+1=0
a = -8; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·(-8)·1
Δ = 816
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{51}}{2*-8}=\frac{28-4\sqrt{51}}{-16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{51}}{2*-8}=\frac{28+4\sqrt{51}}{-16} $
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