-6x2+46x-40=0

Solution for -6x2+46x-40=0 equation:

-6x^2+46x-40=0

a = -6; b = 46; c = -40;
Δ = b2-4ac
Δ = 462-4·(-6)·(-40)
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-34}{2*-6}=\frac{-80}{-12}
=6+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+34}{2*-6}=\frac{-12}{-12}
=1
$