4x^2+17x/3x^2+10x+3=4/3

Solution for 4x^2+17x/3x^2+10x+3=4/3 equation:

4x^2+17x/3x^2+10x+3=4/3

We move all terms to the left:

4x^2+17x/3x^2+10x+3-(4/3)=0


Domain of the equation: 3x^2!=0

x^2!=0/3

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

4x^2+17x/3x^2+10x+3-(+4/3)=0

We add all the numbers together, and all the variables

4x^2+10x+17x/3x^2+3-(+4/3)=0

We get rid of parentheses

4x^2+10x+17x/3x^2+3-4/3=0

We calculate fractions


4x^2+10x+3=0

a = 4; b = 10; c = +3;
Δ = b2-4ac
Δ = 102-4·4·3
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{13}}{2*4}=\frac{-10-2\sqrt{13}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{13}}{2*4}=\frac{-10+2\sqrt{13}}{8}
$