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-6(3/4x-2)+3=-1/2x+7
We move all terms to the left:
-6(3/4x-2)+3-(-1/2x+7)=0
Domain of the equation: 4x-2)!=0
x∈R
Domain of the equation: 2x+7)!=0We multiply parentheses
x∈R
-18x-(-1/2x+7)+12+3=0
We get rid of parentheses
-18x+1/2x-7+12+3=0
We multiply all the terms by the denominator
-18x*2x-7*2x+12*2x+3*2x+1=0
Wy multiply elements
-36x^2-14x+24x+6x+1=0
We add all the numbers together, and all the variables
-36x^2+16x+1=0
a = -36; b = 16; c = +1;
Δ = b2-4ac
Δ = 162-4·(-36)·1
Δ = 400
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{400}=20$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*-36}=\frac{-36}{-72} =1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*-36}=\frac{4}{-72} =-1/18 $
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