(5/8)(24x+8)=25

Solution for (5/8)(24x+8)=25 equation:

(5/8)(24x+8)=25

We move all terms to the left:

(5/8)(24x+8)-(25)=0


Domain of the equation: 8)(24x+8)!=0

x∈R


We add all the numbers together, and all the variables

(+5/8)(24x+8)-25=0

We multiply parentheses ..

(+120x^2+5/8*8)-25=0

We multiply all the terms by the denominator


(+120x^2+5-25*8*8)=0

We get rid of parentheses

120x^2+5-25*8*8=0

We add all the numbers together, and all the variables

120x^2-1595=0

a = 120; b = 0; c = -1595;
Δ = b2-4ac
Δ = 02-4·120·(-1595)
Δ = 765600
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:

$\sqrt{\Delta}=\sqrt{765600}=\sqrt{400*1914}=\sqrt{400}*\sqrt{1914}=20\sqrt{1914}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{1914}}{2*120}=\frac{0-20\sqrt{1914}}{240}
=-\frac{20\sqrt{1914}}{240}
=-\frac{\sqrt{1914}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{1914}}{2*120}=\frac{0+20\sqrt{1914}}{240}
=\frac{20\sqrt{1914}}{240}
=\frac{\sqrt{1914}}{12}
$