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7/4x+x=66
We move all terms to the left:
7/4x+x-(66)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
x+7/4x-66=0
We multiply all the terms by the denominator
x*4x-66*4x+7=0
Wy multiply elements
4x^2-264x+7=0
a = 4; b = -264; c = +7;
Δ = b2-4ac
Δ = -2642-4·4·7
Δ = 69584
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{69584}=\sqrt{16*4349}=\sqrt{16}*\sqrt{4349}=4\sqrt{4349}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-4\sqrt{4349}}{2*4}=\frac{264-4\sqrt{4349}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+4\sqrt{4349}}{2*4}=\frac{264+4\sqrt{4349}}{8} $
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