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1/4x-1.75=1+3x
We move all terms to the left:
1/4x-1.75-(1+3x)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
1/4x-(3x+1)-1.75=0
We get rid of parentheses
1/4x-3x-1-1.75=0
We multiply all the terms by the denominator
-3x*4x-1*4x-(1.75)*4x+1=0
We multiply parentheses
-3x*4x-1*4x-7x+1=0
Wy multiply elements
-12x^2-4x-7x+1=0
We add all the numbers together, and all the variables
-12x^2-11x+1=0
a = -12; b = -11; c = +1;
Δ = b2-4ac
Δ = -112-4·(-12)·1
Δ = 169
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-13}{2*-12}=\frac{-2}{-24} =1/12 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+13}{2*-12}=\frac{24}{-24} =-1 $
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