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.6x-15=6/5x+12
We move all terms to the left:
.6x-15-(6/5x+12)=0
Domain of the equation: 5x+12)!=0We get rid of parentheses
x∈R
.6x-6/5x-12-15=0
We multiply all the terms by the denominator
(.6x)*5x-12*5x-15*5x-6=0
We add all the numbers together, and all the variables
(+.6x)*5x-12*5x-15*5x-6=0
We multiply parentheses
5x^2-12*5x-15*5x-6=0
Wy multiply elements
5x^2-60x-75x-6=0
We add all the numbers together, and all the variables
5x^2-135x-6=0
a = 5; b = -135; c = -6;
Δ = b2-4ac
Δ = -1352-4·5·(-6)
Δ = 18345
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{-(-135)-\sqrt{18345}}{2*5}=\frac{135-\sqrt{18345}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-135)+\sqrt{18345}}{2*5}=\frac{135+\sqrt{18345}}{10} $
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