(-3/8)(x-24)+x=19

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Solution for (-3/8)(x-24)+x=19 equation:



(-3/8)(x-24)+x=19
We move all terms to the left:
(-3/8)(x-24)+x-(19)=0
Domain of the equation: 8)(x-24)!=0
x∈R
We add all the numbers together, and all the variables
x+(-3/8)(x-24)-19=0
We multiply parentheses ..
(-3x^2-3/8*-24)+x-19=0
We multiply all the terms by the denominator
(-3x^2-3+x*8*-24)-19*8*-24)=0
We add all the numbers together, and all the variables
(-3x^2-3+x*8*-24)=0
We get rid of parentheses
-3x^2+x*8*-3-24=0
We add all the numbers together, and all the variables
-3x^2+x*8*-27=0
Wy multiply elements
-3x^2+8x^2-27=0
We add all the numbers together, and all the variables
5x^2-27=0
a = 5; b = 0; c = -27;
Δ = b2-4ac
Δ = 02-4·5·(-27)
Δ = 540
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:
$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{15}}{2*5}=\frac{0-6\sqrt{15}}{10} =-\frac{6\sqrt{15}}{10} =-\frac{3\sqrt{15}}{5} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{15}}{2*5}=\frac{0+6\sqrt{15}}{10} =\frac{6\sqrt{15}}{10} =\frac{3\sqrt{15}}{5} $

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