-2(4x+3)(x-7)=46

Solution for -2(4x+3)(x-7)=46 equation:

-2(4x+3)(x-7)=46

We move all terms to the left:

-2(4x+3)(x-7)-(46)=0

We multiply parentheses ..

-2(+4x^2-28x+3x-21)-46=0

We multiply parentheses

-8x^2+56x-6x+42-46=0

We add all the numbers together, and all the variables

-8x^2+50x-4=0

a = -8; b = 50; c = -4;
Δ = b2-4ac
Δ = 502-4·(-8)·(-4)
Δ = 2372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2372}=\sqrt{4*593}=\sqrt{4}*\sqrt{593}=2\sqrt{593}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{593}}{2*-8}=\frac{-50-2\sqrt{593}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{593}}{2*-8}=\frac{-50+2\sqrt{593}}{-16}
$