X^2+x/3-2.5=0

Solution for X^2+x/3-2.5=0 equation:

X^2+X/3-2.5=0

We multiply all the terms by the denominator


X^2*3+X-(2.5)*3=0

We add all the numbers together, and all the variables

X^2*3+X-7.5=0

Wy multiply elements

3X^2+X-7.5=0

a = 3; b = 1; c = -7.5;
Δ = b2-4ac
Δ = 12-4·3·(-7.5)
Δ = 91
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{-(1)-\sqrt{91}}{2*3}=\frac{-1-\sqrt{91}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{91}}{2*3}=\frac{-1+\sqrt{91}}{6}
$