4x-3/3x=10

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

4x-3/3x=10

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-30x-3=0

a = 12; b = -30; c = -3;
Δ = b2-4ac
Δ = -302-4·12·(-3)
Δ = 1044
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:

$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{29}}{2*12}=\frac{30-6\sqrt{29}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{29}}{2*12}=\frac{30+6\sqrt{29}}{24}
$