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

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}
$