3x*x-5x-40=0

Solution for 3x*x-5x-40=0 equation:

3x*x-5x-40=0

We add all the numbers together, and all the variables

-5x+3x*x-40=0

Wy multiply elements

3x^2-5x-40=0

a = 3; b = -5; c = -40;
Δ = b2-4ac
Δ = -52-4·3·(-40)
Δ = 505
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{-(-5)-\sqrt{505}}{2*3}=\frac{5-\sqrt{505}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{505}}{2*3}=\frac{5+\sqrt{505}}{6}
$