4x(x-3)-5(x+8)=6(x+3)-2

Solution for 4x(x-3)-5(x+8)=6(x+3)-2 equation:

4x(x-3)-5(x+8)=6(x+3)-2

We move all terms to the left:

4x(x-3)-5(x+8)-(6(x+3)-2)=0

We multiply parentheses

4x^2-12x-5x-(6(x+3)-2)-40=0


We calculate terms in parentheses: -(6(x+3)-2), so:

6(x+3)-2

We multiply parentheses

6x+18-2

We add all the numbers together, and all the variables

6x+16

Back to the equation:

-(6x+16)


We add all the numbers together, and all the variables

4x^2-17x-(6x+16)-40=0

We get rid of parentheses

4x^2-17x-6x-16-40=0

We add all the numbers together, and all the variables

4x^2-23x-56=0

a = 4; b = -23; c = -56;
Δ = b2-4ac
Δ = -232-4·4·(-56)
Δ = 1425
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:

$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-5\sqrt{57}}{2*4}=\frac{23-5\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+5\sqrt{57}}{2*4}=\frac{23+5\sqrt{57}}{8}
$