4x+25(24)=4x(24+6x)

Solution for 4x+25(24)=4x(24+6x) equation:

4x+25(24)=4x(24+6x)

We move all terms to the left:

4x+25(24)-(4x(24+6x))=0

We add all the numbers together, and all the variables

4x-(4x(6x+24))+2524=0


We calculate terms in parentheses: -(4x(6x+24)), so:

4x(6x+24)

We multiply parentheses

24x^2+96x

Back to the equation:

-(24x^2+96x)


We get rid of parentheses

-24x^2+4x-96x+2524=0

We add all the numbers together, and all the variables

-24x^2-92x+2524=0

a = -24; b = -92; c = +2524;
Δ = b2-4ac
Δ = -922-4·(-24)·2524
Δ = 250768
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:

$\sqrt{\Delta}=\sqrt{250768}=\sqrt{16*15673}=\sqrt{16}*\sqrt{15673}=4\sqrt{15673}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-4\sqrt{15673}}{2*-24}=\frac{92-4\sqrt{15673}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+4\sqrt{15673}}{2*-24}=\frac{92+4\sqrt{15673}}{-48}
$