6x^2-53x=-40

Solution for 6x^2-53x=-40 equation:

6x^2-53x=-40

We move all terms to the left:

6x^2-53x-(-40)=0

We add all the numbers together, and all the variables

6x^2-53x+40=0

a = 6; b = -53; c = +40;
Δ = b2-4ac
Δ = -532-4·6·40
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-43}{2*6}=\frac{10}{12}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+43}{2*6}=\frac{96}{12}
=8
$