-6a^2+11a=4

Solution for -6a^2+11a=4 equation:

-6a^2+11a=4

We move all terms to the left:

-6a^2+11a-(4)=0

a = -6; b = 11; c = -4;
Δ = b2-4ac
Δ = 112-4·(-6)·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5}{2*-6}=\frac{-16}{-12}
=1+1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5}{2*-6}=\frac{-6}{-12}
=1/2
$