0=2(7x^2-24x-112)

Solution for 0=2(7x^2-24x-112) equation:

0=2(7x^2-24x-112)

We move all terms to the left:

0-(2(7x^2-24x-112))=0

We add all the numbers together, and all the variables

-(2(7x^2-24x-112))=0


We calculate terms in parentheses: -(2(7x^2-24x-112)), so:

2(7x^2-24x-112)

We multiply parentheses

14x^2-48x-224

Back to the equation:

-(14x^2-48x-224)


We get rid of parentheses

-14x^2+48x+224=0

a = -14; b = 48; c = +224;
Δ = b2-4ac
Δ = 482-4·(-14)·224
Δ = 14848
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:

$\sqrt{\Delta}=\sqrt{14848}=\sqrt{256*58}=\sqrt{256}*\sqrt{58}=16\sqrt{58}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-16\sqrt{58}}{2*-14}=\frac{-48-16\sqrt{58}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+16\sqrt{58}}{2*-14}=\frac{-48+16\sqrt{58}}{-28}
$