5(x-1)+16(2x+3)=6x(2x-7)-

Solution for 5(x-1)+16(2x+3)=6x(2x-7)- equation:

5(x-1)+16(2x+3)=6x(2x-7)-

We move all terms to the left:

5(x-1)+16(2x+3)-(6x(2x-7)-)=0

We multiply parentheses

5x+32x-(6x(2x-7)-)-5+48=0


We calculate terms in parentheses: -(6x(2x-7)-), so:

6x(2x-7)-

We add all the numbers together, and all the variables

6x(2x-7)

We multiply parentheses

12x^2-42x

Back to the equation:

-(12x^2-42x)


We add all the numbers together, and all the variables

37x-(12x^2-42x)+43=0

We get rid of parentheses

-12x^2+37x+42x+43=0

We add all the numbers together, and all the variables

-12x^2+79x+43=0

a = -12; b = 79; c = +43;
Δ = b2-4ac
Δ = 792-4·(-12)·43
Δ = 8305
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{-(79)-\sqrt{8305}}{2*-12}=\frac{-79-\sqrt{8305}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(79)+\sqrt{8305}}{2*-12}=\frac{-79+\sqrt{8305}}{-24}
$