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8/x-7=4x
We move all terms to the left:
8/x-7-(4x)=0
Domain of the equation: x!=0We add all the numbers together, and all the variables
x∈R
-4x+8/x-7=0
We multiply all the terms by the denominator
-4x*x-7*x+8=0
We add all the numbers together, and all the variables
-7x-4x*x+8=0
Wy multiply elements
-4x^2-7x+8=0
a = -4; b = -7; c = +8;
Δ = b2-4ac
Δ = -72-4·(-4)·8
Δ = 177
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{-(-7)-\sqrt{177}}{2*-4}=\frac{7-\sqrt{177}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{177}}{2*-4}=\frac{7+\sqrt{177}}{-8} $
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