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7x-11/4x=-121
We move all terms to the left:
7x-11/4x-(-121)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
7x-11/4x+121=0
We multiply all the terms by the denominator
7x*4x+121*4x-11=0
Wy multiply elements
28x^2+484x-11=0
a = 28; b = 484; c = -11;
Δ = b2-4ac
Δ = 4842-4·28·(-11)
Δ = 235488
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{235488}=\sqrt{16*14718}=\sqrt{16}*\sqrt{14718}=4\sqrt{14718}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(484)-4\sqrt{14718}}{2*28}=\frac{-484-4\sqrt{14718}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(484)+4\sqrt{14718}}{2*28}=\frac{-484+4\sqrt{14718}}{56} $
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