6x^2=35-x

Solution for 6x^2=35-x equation:

6x^2=35-x

We move all terms to the left:

6x^2-(35-x)=0

We add all the numbers together, and all the variables

6x^2-(-1x+35)=0

We get rid of parentheses

6x^2+1x-35=0

We add all the numbers together, and all the variables

6x^2+x-35=0

a = 6; b = 1; c = -35;
Δ = b2-4ac
Δ = 12-4·6·(-35)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-29}{2*6}=\frac{-30}{12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+29}{2*6}=\frac{28}{12}
=2+1/3
$