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X+24=5/4X
We move all terms to the left:
X+24-(5/4X)=0
Domain of the equation: 4X)!=0We add all the numbers together, and all the variables
X!=0/1
X!=0
X∈R
X-(+5/4X)+24=0
We get rid of parentheses
X-5/4X+24=0
We multiply all the terms by the denominator
X*4X+24*4X-5=0
Wy multiply elements
4X^2+96X-5=0
a = 4; b = 96; c = -5;
Δ = b2-4ac
Δ = 962-4·4·(-5)
Δ = 9296
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9296}=\sqrt{16*581}=\sqrt{16}*\sqrt{581}=4\sqrt{581}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-4\sqrt{581}}{2*4}=\frac{-96-4\sqrt{581}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+4\sqrt{581}}{2*4}=\frac{-96+4\sqrt{581}}{8} $
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