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(2x+3)-(5x+4)/5x+9=-7/3
We move all terms to the left:
(2x+3)-(5x+4)/5x+9-(-7/3)=0
Domain of the equation: 5x!=0We get rid of parentheses
x!=0/5
x!=0
x∈R
2x-(5x+4)/5x+3+9+7/3=0
We calculate fractions
2x+(-15x-12)/15x+35x/15x+3+9=0
We add all the numbers together, and all the variables
2x+(-15x-12)/15x+35x/15x+12=0
We multiply all the terms by the denominator
2x*15x+(-15x-12)+35x+12*15x=0
We add all the numbers together, and all the variables
35x+2x*15x+(-15x-12)+12*15x=0
Wy multiply elements
30x^2+35x+(-15x-12)+180x=0
We get rid of parentheses
30x^2+35x-15x+180x-12=0
We add all the numbers together, and all the variables
30x^2+200x-12=0
a = 30; b = 200; c = -12;
Δ = b2-4ac
Δ = 2002-4·30·(-12)
Δ = 41440
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{41440}=\sqrt{16*2590}=\sqrt{16}*\sqrt{2590}=4\sqrt{2590}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(200)-4\sqrt{2590}}{2*30}=\frac{-200-4\sqrt{2590}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(200)+4\sqrt{2590}}{2*30}=\frac{-200+4\sqrt{2590}}{60} $
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