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2(x-7)=1/2x-4
We move all terms to the left:
2(x-7)-(1/2x-4)=0
Domain of the equation: 2x-4)!=0We multiply parentheses
x∈R
2x-(1/2x-4)-14=0
We get rid of parentheses
2x-1/2x+4-14=0
We multiply all the terms by the denominator
2x*2x+4*2x-14*2x-1=0
Wy multiply elements
4x^2+8x-28x-1=0
We add all the numbers together, and all the variables
4x^2-20x-1=0
a = 4; b = -20; c = -1;
Δ = b2-4ac
Δ = -202-4·4·(-1)
Δ = 416
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{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{26}}{2*4}=\frac{20-4\sqrt{26}}{8}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{26}}{2*4}=\frac{20+4\sqrt{26}}{8}
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