6x(2x-5)=-(x+4)

Solution for 6x(2x-5)=-(x+4) equation:

6x(2x-5)=-(x+4)

We move all terms to the left:

6x(2x-5)-(-(x+4))=0

We multiply parentheses

12x^2-30x-(-(x+4))=0


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

-(x+4)

We get rid of parentheses

-x-4

We add all the numbers together, and all the variables

-1x-4

Back to the equation:

-(-1x-4)


We get rid of parentheses

12x^2-30x+1x+4=0

We add all the numbers together, and all the variables

12x^2-29x+4=0

a = 12; b = -29; c = +4;
Δ = b2-4ac
Δ = -292-4·12·4
Δ = 649
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{-(-29)-\sqrt{649}}{2*12}=\frac{29-\sqrt{649}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{649}}{2*12}=\frac{29+\sqrt{649}}{24}
$