6x^2=11x+35

Solution for 6x^2=11x+35 equation:

6x^2=11x+35

We move all terms to the left:

6x^2-(11x+35)=0

We get rid of parentheses

6x^2-11x-35=0

a = 6; b = -11; c = -35;
Δ = b2-4ac
Δ = -112-4·6·(-35)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-31}{2*6}=\frac{-20}{12}
=-1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*6}=\frac{42}{12}
=3+1/2
$