4+7x=4x(2x+1)-8

Solution for 4+7x=4x(2x+1)-8 equation:

4+7x=4x(2x+1)-8

We move all terms to the left:

4+7x-(4x(2x+1)-8)=0


We calculate terms in parentheses: -(4x(2x+1)-8), so:

4x(2x+1)-8

We multiply parentheses

8x^2+4x-8

Back to the equation:

-(8x^2+4x-8)


We get rid of parentheses

-8x^2+7x-4x+8+4=0

We add all the numbers together, and all the variables

-8x^2+3x+12=0

a = -8; b = 3; c = +12;
Δ = b2-4ac
Δ = 32-4·(-8)·12
Δ = 393
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{-(3)-\sqrt{393}}{2*-8}=\frac{-3-\sqrt{393}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{393}}{2*-8}=\frac{-3+\sqrt{393}}{-16}
$