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2x+7=2/5x+15
We move all terms to the left:
2x+7-(2/5x+15)=0
Domain of the equation: 5x+15)!=0We get rid of parentheses
x∈R
2x-2/5x-15+7=0
We multiply all the terms by the denominator
2x*5x-15*5x+7*5x-2=0
Wy multiply elements
10x^2-75x+35x-2=0
We add all the numbers together, and all the variables
10x^2-40x-2=0
a = 10; b = -40; c = -2;
Δ = b2-4ac
Δ = -402-4·10·(-2)
Δ = 1680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-4\sqrt{105}}{2*10}=\frac{40-4\sqrt{105}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+4\sqrt{105}}{2*10}=\frac{40+4\sqrt{105}}{20} $
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