3x(2x-7)=-5(2x-12)

Solution for 3x(2x-7)=-5(2x-12) equation:

3x(2x-7)=-5(2x-12)

We move all terms to the left:

3x(2x-7)-(-5(2x-12))=0

We multiply parentheses

6x^2-21x-(-5(2x-12))=0


We calculate terms in parentheses: -(-5(2x-12)), so:

-5(2x-12)

We multiply parentheses

-10x+60

Back to the equation:

-(-10x+60)


We get rid of parentheses

6x^2-21x+10x-60=0

We add all the numbers together, and all the variables

6x^2-11x-60=0

a = 6; b = -11; c = -60;
Δ = b2-4ac
Δ = -112-4·6·(-60)
Δ = 1561
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{-(-11)-\sqrt{1561}}{2*6}=\frac{11-\sqrt{1561}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{1561}}{2*6}=\frac{11+\sqrt{1561}}{12}
$