6x2=5-2x

Solution for 6x2=5-2x equation:

6x^2=5-2x

We move all terms to the left:

6x^2-(5-2x)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

6x^2+2x-5=0

a = 6; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·6·(-5)
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{31}}{2*6}=\frac{-2-2\sqrt{31}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{31}}{2*6}=\frac{-2+2\sqrt{31}}{12}
$