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-3/4x-8=x
We move all terms to the left:
-3/4x-8-(x)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
-1x-3/4x-8=0
We multiply all the terms by the denominator
-1x*4x-8*4x-3=0
Wy multiply elements
-4x^2-32x-3=0
a = -4; b = -32; c = -3;
Δ = b2-4ac
Δ = -322-4·(-4)·(-3)
Δ = 976
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{976}=\sqrt{16*61}=\sqrt{16}*\sqrt{61}=4\sqrt{61}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{61}}{2*-4}=\frac{32-4\sqrt{61}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{61}}{2*-4}=\frac{32+4\sqrt{61}}{-8} $
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