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2/5x+x=90
We move all terms to the left:
2/5x+x-(90)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
x+2/5x-90=0
We multiply all the terms by the denominator
x*5x-90*5x+2=0
Wy multiply elements
5x^2-450x+2=0
a = 5; b = -450; c = +2;
Δ = b2-4ac
Δ = -4502-4·5·2
Δ = 202460
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{202460}=\sqrt{4*50615}=\sqrt{4}*\sqrt{50615}=2\sqrt{50615}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-450)-2\sqrt{50615}}{2*5}=\frac{450-2\sqrt{50615}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-450)+2\sqrt{50615}}{2*5}=\frac{450+2\sqrt{50615}}{10} $
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