5-(x-3)=4x(3x-8)

Solution for 5-(x-3)=4x(3x-8) equation:

5-(x-3)=4x(3x-8)

We move all terms to the left:

5-(x-3)-(4x(3x-8))=0

We get rid of parentheses

-x-(4x(3x-8))+3+5=0


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

4x(3x-8)

We multiply parentheses

12x^2-32x

Back to the equation:

-(12x^2-32x)


We add all the numbers together, and all the variables

-1x-(12x^2-32x)+8=0

We get rid of parentheses

-12x^2-1x+32x+8=0

We add all the numbers together, and all the variables

-12x^2+31x+8=0

a = -12; b = 31; c = +8;
Δ = b2-4ac
Δ = 312-4·(-12)·8
Δ = 1345
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{-(31)-\sqrt{1345}}{2*-12}=\frac{-31-\sqrt{1345}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{1345}}{2*-12}=\frac{-31+\sqrt{1345}}{-24}
$