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2.5x+18=3/5x-4
We move all terms to the left:
2.5x+18-(3/5x-4)=0
Domain of the equation: 5x-4)!=0We get rid of parentheses
x∈R
2.5x-3/5x+4+18=0
We multiply all the terms by the denominator
(2.5x)*5x+4*5x+18*5x-3=0
We add all the numbers together, and all the variables
(+2.5x)*5x+4*5x+18*5x-3=0
We multiply parentheses
10x^2+4*5x+18*5x-3=0
Wy multiply elements
10x^2+20x+90x-3=0
We add all the numbers together, and all the variables
10x^2+110x-3=0
a = 10; b = 110; c = -3;
Δ = b2-4ac
Δ = 1102-4·10·(-3)
Δ = 12220
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12220}=\sqrt{4*3055}=\sqrt{4}*\sqrt{3055}=2\sqrt{3055}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-2\sqrt{3055}}{2*10}=\frac{-110-2\sqrt{3055}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+2\sqrt{3055}}{2*10}=\frac{-110+2\sqrt{3055}}{20} $
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