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7/10x+3x=17
We move all terms to the left:
7/10x+3x-(17)=0
Domain of the equation: 10x!=0We add all the numbers together, and all the variables
x!=0/10
x!=0
x∈R
3x+7/10x-17=0
We multiply all the terms by the denominator
3x*10x-17*10x+7=0
Wy multiply elements
30x^2-170x+7=0
a = 30; b = -170; c = +7;
Δ = b2-4ac
Δ = -1702-4·30·7
Δ = 28060
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{28060}=\sqrt{4*7015}=\sqrt{4}*\sqrt{7015}=2\sqrt{7015}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-2\sqrt{7015}}{2*30}=\frac{170-2\sqrt{7015}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+2\sqrt{7015}}{2*30}=\frac{170+2\sqrt{7015}}{60} $
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