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-9.95-3/2x=-5-6.5x
We move all terms to the left:
-9.95-3/2x-(-5-6.5x)=0
Domain of the equation: 2x!=0We add all the numbers together, and all the variables
x!=0/2
x!=0
x∈R
-3/2x-(-6.5x-5)-9.95=0
We get rid of parentheses
-3/2x+6.5x+5-9.95=0
We multiply all the terms by the denominator
(6.5x)*2x+5*2x-(9.95)*2x-3=0
We add all the numbers together, and all the variables
(+6.5x)*2x+5*2x-(9.95)*2x-3=0
We multiply parentheses
12x^2+5*2x-19.9x-3=0
Wy multiply elements
12x^2+10x-19.9x-3=0
We add all the numbers together, and all the variables
12x^2-9.9x-3=0
a = 12; b = -9.9; c = -3;
Δ = b2-4ac
Δ = -9.92-4·12·(-3)
Δ = 242.01
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{-(-9.9)-\sqrt{242.01}}{2*12}=\frac{9.9-\sqrt{242.01}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9.9)+\sqrt{242.01}}{2*12}=\frac{9.9+\sqrt{242.01}}{24} $
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