x^2+4x-5x/3-1=0

Solution for x^2+4x-5x/3-1=0 equation:

x^2+4x-5x/3-1=0

We multiply all the terms by the denominator


x^2*3+4x*3-5x-1*3=0

We add all the numbers together, and all the variables

x^2*3-5x+4x*3-3=0

Wy multiply elements

3x^2-5x+12x-3=0

We add all the numbers together, and all the variables

3x^2+7x-3=0

a = 3; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·3·(-3)
Δ = 85
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{85}}{2*3}=\frac{-7-\sqrt{85}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{85}}{2*3}=\frac{-7+\sqrt{85}}{6}
$