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x=8/5x-21
We move all terms to the left:
x-(8/5x-21)=0
Domain of the equation: 5x-21)!=0We get rid of parentheses
x∈R
x-8/5x+21=0
We multiply all the terms by the denominator
x*5x+21*5x-8=0
Wy multiply elements
5x^2+105x-8=0
a = 5; b = 105; c = -8;
Δ = b2-4ac
Δ = 1052-4·5·(-8)
Δ = 11185
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{-(105)-\sqrt{11185}}{2*5}=\frac{-105-\sqrt{11185}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{11185}}{2*5}=\frac{-105+\sqrt{11185}}{10} $
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