2/5x+x=70

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Solution for 2/5x+x=70 equation: 



2/5x+x=70

We move all terms to the left:

2/5x+x-(70)=0



Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



We add all the numbers together, and all the variables

x+2/5x-70=0

We multiply all the terms by the denominator


x*5x-70*5x+2=0

Wy multiply elements

5x^2-350x+2=0

a = 5; b = -350; c = +2;
Δ = b2-4ac
Δ = -3502-4·5·2
Δ = 122460
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:


$\sqrt{\Delta}=\sqrt{122460}=\sqrt{4*30615}=\sqrt{4}*\sqrt{30615}=2\sqrt{30615}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-2\sqrt{30615}}{2*5}=\frac{350-2\sqrt{30615}}{10}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+2\sqrt{30615}}{2*5}=\frac{350+2\sqrt{30615}}{10}
$

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