4-(2x+3)=7x(2x+12)

Solution for 4-(2x+3)=7x(2x+12) equation:

4-(2x+3)=7x(2x+12)

We move all terms to the left:

4-(2x+3)-(7x(2x+12))=0

We get rid of parentheses

-2x-(7x(2x+12))-3+4=0


We calculate terms in parentheses: -(7x(2x+12)), so:

7x(2x+12)

We multiply parentheses

14x^2+84x

Back to the equation:

-(14x^2+84x)


We add all the numbers together, and all the variables

-2x-(14x^2+84x)+1=0

We get rid of parentheses

-14x^2-2x-84x+1=0

We add all the numbers together, and all the variables

-14x^2-86x+1=0

a = -14; b = -86; c = +1;
Δ = b2-4ac
Δ = -862-4·(-14)·1
Δ = 7452
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:

$\sqrt{\Delta}=\sqrt{7452}=\sqrt{324*23}=\sqrt{324}*\sqrt{23}=18\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-18\sqrt{23}}{2*-14}=\frac{86-18\sqrt{23}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+18\sqrt{23}}{2*-14}=\frac{86+18\sqrt{23}}{-28}
$