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X=8/5X+28
We move all terms to the left:
X-(8/5X+28)=0
Domain of the equation: 5X+28)!=0We get rid of parentheses
X∈R
X-8/5X-28=0
We multiply all the terms by the denominator
X*5X-28*5X-8=0
Wy multiply elements
5X^2-140X-8=0
a = 5; b = -140; c = -8;
Δ = b2-4ac
Δ = -1402-4·5·(-8)
Δ = 19760
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{19760}=\sqrt{16*1235}=\sqrt{16}*\sqrt{1235}=4\sqrt{1235}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-4\sqrt{1235}}{2*5}=\frac{140-4\sqrt{1235}}{10} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+4\sqrt{1235}}{2*5}=\frac{140+4\sqrt{1235}}{10} $
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