-3x^2+11x=8

Solution for -3x^2+11x=8 equation:

-3x^2+11x=8

We move all terms to the left:

-3x^2+11x-(8)=0

a = -3; b = 11; c = -8;
Δ = b2-4ac
Δ = 112-4·(-3)·(-8)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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