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3/5x+5x=70
We move all terms to the left:
3/5x+5x-(70)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
5x+3/5x-70=0
We multiply all the terms by the denominator
5x*5x-70*5x+3=0
Wy multiply elements
25x^2-350x+3=0
a = 25; b = -350; c = +3;
Δ = b2-4ac
Δ = -3502-4·25·3
Δ = 122200
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{122200}=\sqrt{100*1222}=\sqrt{100}*\sqrt{1222}=10\sqrt{1222}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-10\sqrt{1222}}{2*25}=\frac{350-10\sqrt{1222}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+10\sqrt{1222}}{2*25}=\frac{350+10\sqrt{1222}}{50} $
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