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7x-4/4x=31
We move all terms to the left:
7x-4/4x-(31)=0
Domain of the equation: 4x!=0We multiply all the terms by the denominator
x!=0/4
x!=0
x∈R
7x*4x-31*4x-4=0
Wy multiply elements
28x^2-124x-4=0
a = 28; b = -124; c = -4;
Δ = b2-4ac
Δ = -1242-4·28·(-4)
Δ = 15824
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{15824}=\sqrt{16*989}=\sqrt{16}*\sqrt{989}=4\sqrt{989}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-4\sqrt{989}}{2*28}=\frac{124-4\sqrt{989}}{56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+4\sqrt{989}}{2*28}=\frac{124+4\sqrt{989}}{56} $
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