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-5x+1/2x-4=-13

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Solution for -5x+1/2x-4=-13 equation:



-5x+1/2x-4=-13
We move all terms to the left:
-5x+1/2x-4-(-13)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We add all the numbers together, and all the variables
-5x+1/2x+9=0
We multiply all the terms by the denominator
-5x*2x+9*2x+1=0
Wy multiply elements
-10x^2+18x+1=0
a = -10; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·(-10)·1
Δ = 364
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}

The end solution:
\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{91}}{2*-10}=\frac{-18-2\sqrt{91}}{-20}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{91}}{2*-10}=\frac{-18+2\sqrt{91}}{-20}

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