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5(2.5x-6)=25/2x-4.8
We move all terms to the left:
5(2.5x-6)-(25/2x-4.8)=0
Domain of the equation: 2x-4.8)!=0We multiply parentheses
x∈R
10x-(25/2x-4.8)-30=0
We get rid of parentheses
10x-25/2x+4.8-30=0
We multiply all the terms by the denominator
10x*2x+(4.8)*2x-30*2x-25=0
We multiply parentheses
10x*2x+9.6x-30*2x-25=0
Wy multiply elements
20x^2+9.6x-60x-25=0
We add all the numbers together, and all the variables
20x^2-50.4x-25=0
a = 20; b = -50.4; c = -25;
Δ = b2-4ac
Δ = -50.42-4·20·(-25)
Δ = 4540.16
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{-(-50.4)-\sqrt{4540.16}}{2*20}=\frac{50.4-\sqrt{4540.16}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50.4)+\sqrt{4540.16}}{2*20}=\frac{50.4+\sqrt{4540.16}}{40} $
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