4x=8(2x-3)4x-16x-3

Solution for 4x=8(2x-3)4x-16x-3 equation:

4x=8(2x-3)4x-16x-3

We move all terms to the left:

4x-(8(2x-3)4x-16x-3)=0


We calculate terms in parentheses: -(8(2x-3)4x-16x-3), so:

8(2x-3)4x-16x-3

We add all the numbers together, and all the variables

-16x+8(2x-3)4x-3

We multiply parentheses

64x^2-16x-96x-3

We add all the numbers together, and all the variables

64x^2-112x-3

Back to the equation:

-(64x^2-112x-3)


We get rid of parentheses

-64x^2+4x+112x+3=0

We add all the numbers together, and all the variables

-64x^2+116x+3=0

a = -64; b = 116; c = +3;
Δ = b2-4ac
Δ = 1162-4·(-64)·3
Δ = 14224
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:

$\sqrt{\Delta}=\sqrt{14224}=\sqrt{16*889}=\sqrt{16}*\sqrt{889}=4\sqrt{889}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(116)-4\sqrt{889}}{2*-64}=\frac{-116-4\sqrt{889}}{-128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(116)+4\sqrt{889}}{2*-64}=\frac{-116+4\sqrt{889}}{-128}
$