x^2+5x/6=4

Solution for x^2+5x/6=4 equation:

x^2+5x/6=4

We move all terms to the left:

x^2+5x/6-(4)=0

We multiply all the terms by the denominator


x^2*6+5x-4*6=0

We add all the numbers together, and all the variables

x^2*6+5x-24=0

Wy multiply elements

6x^2+5x-24=0

a = 6; b = 5; c = -24;
Δ = b2-4ac
Δ = 52-4·6·(-24)
Δ = 601
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{-(5)-\sqrt{601}}{2*6}=\frac{-5-\sqrt{601}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{601}}{2*6}=\frac{-5+\sqrt{601}}{12}
$