7x-3x^2=-40

Solution for 7x-3x^2=-40 equation:

7x-3x^2=-40

We move all terms to the left:

7x-3x^2-(-40)=0

We add all the numbers together, and all the variables

-3x^2+7x+40=0

a = -3; b = 7; c = +40;
Δ = b2-4ac
Δ = 72-4·(-3)·40
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*-3}=\frac{-30}{-6}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*-3}=\frac{16}{-6}
=-2+2/3
$