6x^2=43x-40=0

Solution for 6x^2=43x-40=0 equation:

6x^2=43x-40=0

We move all terms to the left:

6x^2-(43x-40)=0

We get rid of parentheses

6x^2-43x+40=0

a = 6; b = -43; c = +40;
Δ = b2-4ac
Δ = -432-4·6·40
Δ = 889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-43)-\sqrt{889}}{2*6}=\frac{43-\sqrt{889}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-43)+\sqrt{889}}{2*6}=\frac{43+\sqrt{889}}{12}
$