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2/5x+1=4x+3
We move all terms to the left:
2/5x+1-(4x+3)=0
Domain of the equation: 5x!=0We get rid of parentheses
x!=0/5
x!=0
x∈R
2/5x-4x-3+1=0
We multiply all the terms by the denominator
-4x*5x-3*5x+1*5x+2=0
Wy multiply elements
-20x^2-15x+5x+2=0
We add all the numbers together, and all the variables
-20x^2-10x+2=0
a = -20; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·(-20)·2
Δ = 260
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{65}}{2*-20}=\frac{10-2\sqrt{65}}{-40} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{65}}{2*-20}=\frac{10+2\sqrt{65}}{-40} $
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