6x^2=20-58x

Solution for 6x^2=20-58x equation:

6x^2=20-58x

We move all terms to the left:

6x^2-(20-58x)=0

We add all the numbers together, and all the variables

6x^2-(-58x+20)=0

We get rid of parentheses

6x^2+58x-20=0

a = 6; b = 58; c = -20;
Δ = b2-4ac
Δ = 582-4·6·(-20)
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-62}{2*6}=\frac{-120}{12}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+62}{2*6}=\frac{4}{12}
=1/3
$