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2/5x+15=2x-8
We move all terms to the left:
2/5x+15-(2x-8)=0
Domain of the equation: 5x!=0We get rid of parentheses
x!=0/5
x!=0
x∈R
2/5x-2x+8+15=0
We multiply all the terms by the denominator
-2x*5x+8*5x+15*5x+2=0
Wy multiply elements
-10x^2+40x+75x+2=0
We add all the numbers together, and all the variables
-10x^2+115x+2=0
a = -10; b = 115; c = +2;
Δ = b2-4ac
Δ = 1152-4·(-10)·2
Δ = 13305
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(115)-\sqrt{13305}}{2*-10}=\frac{-115-\sqrt{13305}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(115)+\sqrt{13305}}{2*-10}=\frac{-115+\sqrt{13305}}{-20} $
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