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2/5x-7=3x-4
We move all terms to the left:
2/5x-7-(3x-4)=0
Domain of the equation: 5x!=0We get rid of parentheses
x!=0/5
x!=0
x∈R
2/5x-3x+4-7=0
We multiply all the terms by the denominator
-3x*5x+4*5x-7*5x+2=0
Wy multiply elements
-15x^2+20x-35x+2=0
We add all the numbers together, and all the variables
-15x^2-15x+2=0
a = -15; b = -15; c = +2;
Δ = b2-4ac
Δ = -152-4·(-15)·2
Δ = 345
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{-(-15)-\sqrt{345}}{2*-15}=\frac{15-\sqrt{345}}{-30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{345}}{2*-15}=\frac{15+\sqrt{345}}{-30} $
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