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32x-1/4x+5=6.95
We move all terms to the left:
32x-1/4x+5-(6.95)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
32x-1/4x-1.95=0
We multiply all the terms by the denominator
32x*4x-(1.95)*4x-1=0
We multiply parentheses
32x*4x-7.8x-1=0
Wy multiply elements
128x^2-7.8x-1=0
a = 128; b = -7.8; c = -1;
Δ = b2-4ac
Δ = -7.82-4·128·(-1)
Δ = 572.84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7.8)-\sqrt{572.84}}{2*128}=\frac{7.8-\sqrt{572.84}}{256} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.8)+\sqrt{572.84}}{2*128}=\frac{7.8+\sqrt{572.84}}{256} $
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