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X/10X-2(3X+5)=6
We move all terms to the left:
X/10X-2(3X+5)-(6)=0
Domain of the equation: 10X!=0We multiply parentheses
X!=0/10
X!=0
X∈R
X/10X-6X-10-6=0
We multiply all the terms by the denominator
X-6X*10X-10*10X-6*10X=0
Wy multiply elements
-60X^2+X-100X-60X=0
We add all the numbers together, and all the variables
-60X^2-159X=0
a = -60; b = -159; c = 0;
Δ = b2-4ac
Δ = -1592-4·(-60)·0
Δ = 25281
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{25281}=159$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-159)-159}{2*-60}=\frac{0}{-120} =0 $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-159)+159}{2*-60}=\frac{318}{-120} =-2+13/20 $
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