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1/4x-3/8x=10
We move all terms to the left:
1/4x-3/8x-(10)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
Domain of the equation: 8x!=0We calculate fractions
x!=0/8
x!=0
x∈R
8x/32x^2+(-12x)/32x^2-10=0
We multiply all the terms by the denominator
8x+(-12x)-10*32x^2=0
Wy multiply elements
-320x^2+8x+(-12x)=0
We get rid of parentheses
-320x^2+8x-12x=0
We add all the numbers together, and all the variables
-320x^2-4x=0
a = -320; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-320)·0
Δ = 16
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{16}=4$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-320}=\frac{0}{-640} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-320}=\frac{8}{-640} =-1/80 $
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