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3-5/6x=7+5/8x
We move all terms to the left:
3-5/6x-(7+5/8x)=0
Domain of the equation: 6x!=0
x!=0/6
x!=0
x∈R
Domain of the equation: 8x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
-5/6x-(5/8x+7)+3=0
We get rid of parentheses
-5/6x-5/8x-7+3=0
We calculate fractions
(-40x)/48x^2+(-30x)/48x^2-7+3=0
We add all the numbers together, and all the variables
(-40x)/48x^2+(-30x)/48x^2-4=0
We multiply all the terms by the denominator
(-40x)+(-30x)-4*48x^2=0
Wy multiply elements
-192x^2+(-40x)+(-30x)=0
We get rid of parentheses
-192x^2-40x-30x=0
We add all the numbers together, and all the variables
-192x^2-70x=0
a = -192; b = -70; c = 0;
Δ = b2-4ac
Δ = -702-4·(-192)·0
Δ = 4900
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{4900}=70$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-70}{2*-192}=\frac{0}{-384} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+70}{2*-192}=\frac{140}{-384} =-35/96 $
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