24x-4/3x=10

Solution for 24x-4/3x=10 equation:

24x-4/3x=10

We move all terms to the left:

24x-4/3x-(10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


24x*3x-10*3x-4=0

Wy multiply elements

72x^2-30x-4=0

a = 72; b = -30; c = -4;
Δ = b2-4ac
Δ = -302-4·72·(-4)
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{57}}{2*72}=\frac{30-6\sqrt{57}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{57}}{2*72}=\frac{30+6\sqrt{57}}{144}
$