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3/4x+x=152
We move all terms to the left:
3/4x+x-(152)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
x+3/4x-152=0
We multiply all the terms by the denominator
x*4x-152*4x+3=0
Wy multiply elements
4x^2-608x+3=0
a = 4; b = -608; c = +3;
Δ = b2-4ac
Δ = -6082-4·4·3
Δ = 369616
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{369616}=\sqrt{16*23101}=\sqrt{16}*\sqrt{23101}=4\sqrt{23101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-608)-4\sqrt{23101}}{2*4}=\frac{608-4\sqrt{23101}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-608)+4\sqrt{23101}}{2*4}=\frac{608+4\sqrt{23101}}{8} $
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