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1/2x+2=0.75x
We move all terms to the left:
1/2x+2-(0.75x)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
1/2x-(+0.75x)+2=0
We get rid of parentheses
1/2x-0.75x+2=0
We multiply all the terms by the denominator
-(0.75x)*2x+2*2x+1=0
We add all the numbers together, and all the variables
-(+0.75x)*2x+2*2x+1=0
We multiply parentheses
-0x^2+2*2x+1=0
Wy multiply elements
-0x^2+4x+1=0
We add all the numbers together, and all the variables
-1x^2+4x+1=0
a = -1; b = 4; c = +1;
Δ = b2-4ac
Δ = 42-4·(-1)·1
Δ = 20
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{5}}{2*-1}=\frac{-4-2\sqrt{5}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{5}}{2*-1}=\frac{-4+2\sqrt{5}}{-2} $
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