5x2-11x-39=3

Solution for 5x2-11x-39=3 equation:

5x^2-11x-39=3

We move all terms to the left:

5x^2-11x-39-(3)=0

We add all the numbers together, and all the variables

5x^2-11x-42=0

a = 5; b = -11; c = -42;
Δ = b2-4ac
Δ = -112-4·5·(-42)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-31}{2*5}=\frac{-20}{10}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+31}{2*5}=\frac{42}{10}
=4+1/5
$