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2/5y+y=70
We move all terms to the left:
2/5y+y-(70)=0
Domain of the equation: 5y!=0We add all the numbers together, and all the variables
y!=0/5
y!=0
y∈R
y+2/5y-70=0
We multiply all the terms by the denominator
y*5y-70*5y+2=0
Wy multiply elements
5y^2-350y+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:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{122460}=\sqrt{4*30615}=\sqrt{4}*\sqrt{30615}=2\sqrt{30615}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-350)-2\sqrt{30615}}{2*5}=\frac{350-2\sqrt{30615}}{10} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-350)+2\sqrt{30615}}{2*5}=\frac{350+2\sqrt{30615}}{10} $
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