2(4x-6)-5x(x-7)=24

Solution for 2(4x-6)-5x(x-7)=24 equation:

2(4x-6)-5x(x-7)=24

We move all terms to the left:

2(4x-6)-5x(x-7)-(24)=0

We multiply parentheses

-5x^2+8x+35x-12-24=0

We add all the numbers together, and all the variables

-5x^2+43x-36=0

a = -5; b = 43; c = -36;
Δ = b2-4ac
Δ = 432-4·(-5)·(-36)
Δ = 1129
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{-(43)-\sqrt{1129}}{2*-5}=\frac{-43-\sqrt{1129}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+\sqrt{1129}}{2*-5}=\frac{-43+\sqrt{1129}}{-10}
$