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/2x+5=4x+13
We move all terms to the left:
/2x+5-(4x+13)=0
Domain of the equation: 2x!=0We get rid of parentheses
x!=0/2
x!=0
x∈R
/2x-4x-13+5=0
We multiply all the terms by the denominator
-4x*2x-13*2x+5*2x+=0
We add all the numbers together, and all the variables
-4x*2x-13*2x+5*2x=0
Wy multiply elements
-8x^2-26x+10x=0
We add all the numbers together, and all the variables
-8x^2-16x=0
a = -8; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·(-8)·0
Δ = 256
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{256}=16$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*-8}=\frac{0}{-16} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*-8}=\frac{32}{-16} =-2 $
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