2x^2-5x-12=77*40

Solution for 2x^2-5x-12=77*40 equation:

2x^2-5x-12=77*40

We move all terms to the left:

2x^2-5x-12-(77*40)=0

We add all the numbers together, and all the variables

2x^2-5x-12-3080=0

We add all the numbers together, and all the variables

2x^2-5x-3092=0

a = 2; b = -5; c = -3092;
Δ = b2-4ac
Δ = -52-4·2·(-3092)
Δ = 24761
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{24761}}{2*2}=\frac{5-\sqrt{24761}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{24761}}{2*2}=\frac{5+\sqrt{24761}}{4}
$