10x-24=1/4(24x)+64

Solution for 10x-24=1/4(24x)+64 equation:

10x-24=1/4(24x)+64

We move all terms to the left:

10x-24-(1/4(24x)+64)=0


Domain of the equation: 424x+64)!=0

x∈R


We get rid of parentheses

10x-1/424x-64-24=0

We multiply all the terms by the denominator


10x*424x-64*424x-24*424x-1=0

Wy multiply elements

4240x^2-27136x-10176x-1=0

We add all the numbers together, and all the variables

4240x^2-37312x-1=0

a = 4240; b = -37312; c = -1;
Δ = b2-4ac
Δ = -373122-4·4240·(-1)
Δ = 1392202304
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:

$\sqrt{\Delta}=\sqrt{1392202304}=\sqrt{64*21753161}=\sqrt{64}*\sqrt{21753161}=8\sqrt{21753161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37312)-8\sqrt{21753161}}{2*4240}=\frac{37312-8\sqrt{21753161}}{8480}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37312)+8\sqrt{21753161}}{2*4240}=\frac{37312+8\sqrt{21753161}}{8480}
$