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.3=-4x+5/5x-4
We move all terms to the left:
.3-(-4x+5/5x-4)=0
Domain of the equation: 5x-4)!=0We add all the numbers together, and all the variables
x∈R
-(-4x+5/5x-4)+0.3=0
We get rid of parentheses
4x-5/5x+4+0.3=0
We multiply all the terms by the denominator
4x*5x+4*5x+(0.3)*5x-5=0
We multiply parentheses
4x*5x+4*5x+1.5x-5=0
Wy multiply elements
20x^2+20x+1.5x-5=0
We add all the numbers together, and all the variables
20x^2+21.5x-5=0
a = 20; b = 21.5; c = -5;
Δ = b2-4ac
Δ = 21.52-4·20·(-5)
Δ = 862.25
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{-(21.5)-\sqrt{862.25}}{2*20}=\frac{-21.5-\sqrt{862.25}}{40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21.5)+\sqrt{862.25}}{2*20}=\frac{-21.5+\sqrt{862.25}}{40} $
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