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2x-1=3/4x=9

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Solution for 2x-1=3/4x=9 equation:



2x-1=3/4x=9
We move all terms to the left:
2x-1-(3/4x)=0
Domain of the equation: 4x)!=0
x!=0/1
x!=0
x∈R
We add all the numbers together, and all the variables
2x-(+3/4x)-1=0
We get rid of parentheses
2x-3/4x-1=0
We multiply all the terms by the denominator
2x*4x-1*4x-3=0
Wy multiply elements
8x^2-4x-3=0
a = 8; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·8·(-3)
Δ = 112
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{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{7}}{2*8}=\frac{4-4\sqrt{7}}{16}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{7}}{2*8}=\frac{4+4\sqrt{7}}{16}

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