13-(x+5)=4x(6x-5)

Solution for 13-(x+5)=4x(6x-5) equation:

13-(x+5)=4x(6x-5)

We move all terms to the left:

13-(x+5)-(4x(6x-5))=0

We get rid of parentheses

-x-(4x(6x-5))-5+13=0


We calculate terms in parentheses: -(4x(6x-5)), so:

4x(6x-5)

We multiply parentheses

24x^2-20x

Back to the equation:

-(24x^2-20x)


We add all the numbers together, and all the variables

-1x-(24x^2-20x)+8=0

We get rid of parentheses

-24x^2-1x+20x+8=0

We add all the numbers together, and all the variables

-24x^2+19x+8=0

a = -24; b = 19; c = +8;
Δ = b2-4ac
Δ = 192-4·(-24)·8
Δ = 1129
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{-(19)-\sqrt{1129}}{2*-24}=\frac{-19-\sqrt{1129}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{1129}}{2*-24}=\frac{-19+\sqrt{1129}}{-48}
$