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5/4x=6-2.5x
We move all terms to the left:
5/4x-(6-2.5x)=0
Domain of the equation: 4x!=0We add all the numbers together, and all the variables
x!=0/4
x!=0
x∈R
5/4x-(-2.5x+6)=0
We get rid of parentheses
5/4x+2.5x-6=0
We multiply all the terms by the denominator
(2.5x)*4x-6*4x+5=0
We add all the numbers together, and all the variables
(+2.5x)*4x-6*4x+5=0
We multiply parentheses
8x^2-6*4x+5=0
Wy multiply elements
8x^2-24x+5=0
a = 8; b = -24; c = +5;
Δ = b2-4ac
Δ = -242-4·8·5
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{-(-24)-4\sqrt{26}}{2*8}=\frac{24-4\sqrt{26}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{26}}{2*8}=\frac{24+4\sqrt{26}}{16} $
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