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3/4x+2x=5
We move all terms to the left:
3/4x+2x-(5)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
2x+3/4x-5=0
We multiply all the terms by the denominator
2x*4x-5*4x+3=0
Wy multiply elements
8x^2-20x+3=0
a = 8; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·8·3
Δ = 304
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{19}}{2*8}=\frac{20-4\sqrt{19}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{19}}{2*8}=\frac{20+4\sqrt{19}}{16} $
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