-11x+7=6x^2

Solution for -11x+7=6x^2 equation:

-11x+7=6x^2

We move all terms to the left:

-11x+7-(6x^2)=0

determiningTheFunctionDomain
-6x^2-11x+7=0

a = -6; b = -11; c = +7;
Δ = b2-4ac
Δ = -112-4·(-6)·7
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-17}{2*-6}=\frac{-6}{-12}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+17}{2*-6}=\frac{28}{-12}
=-2+1/3
$