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3/4x=x+12
We move all terms to the left:
3/4x-(x+12)=0
Domain of the equation: 4x!=0We get rid of parentheses
x!=0/4
x!=0
x∈R
3/4x-x-12=0
We multiply all the terms by the denominator
-x*4x-12*4x+3=0
Wy multiply elements
-4x^2-48x+3=0
a = -4; b = -48; c = +3;
Δ = b2-4ac
Δ = -482-4·(-4)·3
Δ = 2352
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2352}=\sqrt{784*3}=\sqrt{784}*\sqrt{3}=28\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-28\sqrt{3}}{2*-4}=\frac{48-28\sqrt{3}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+28\sqrt{3}}{2*-4}=\frac{48+28\sqrt{3}}{-8} $
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