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4/5x=2x-53
We move all terms to the left:
4/5x-(2x-53)=0
Domain of the equation: 5x!=0We get rid of parentheses
x!=0/5
x!=0
x∈R
4/5x-2x+53=0
We multiply all the terms by the denominator
-2x*5x+53*5x+4=0
Wy multiply elements
-10x^2+265x+4=0
a = -10; b = 265; c = +4;
Δ = b2-4ac
Δ = 2652-4·(-10)·4
Δ = 70385
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{-(265)-\sqrt{70385}}{2*-10}=\frac{-265-\sqrt{70385}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(265)+\sqrt{70385}}{2*-10}=\frac{-265+\sqrt{70385}}{-20} $
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