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5x+5=2/10x+29
We move all terms to the left:
5x+5-(2/10x+29)=0
Domain of the equation: 10x+29)!=0We get rid of parentheses
x∈R
5x-2/10x-29+5=0
We multiply all the terms by the denominator
5x*10x-29*10x+5*10x-2=0
Wy multiply elements
50x^2-290x+50x-2=0
We add all the numbers together, and all the variables
50x^2-240x-2=0
a = 50; b = -240; c = -2;
Δ = b2-4ac
Δ = -2402-4·50·(-2)
Δ = 58000
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{58000}=\sqrt{400*145}=\sqrt{400}*\sqrt{145}=20\sqrt{145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-240)-20\sqrt{145}}{2*50}=\frac{240-20\sqrt{145}}{100} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-240)+20\sqrt{145}}{2*50}=\frac{240+20\sqrt{145}}{100} $
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