-7x(3x+11)=-6(5-3x)

Solution for -7x(3x+11)=-6(5-3x) equation:

-7x(3x+11)=-6(5-3x)

We move all terms to the left:

-7x(3x+11)-(-6(5-3x))=0

We add all the numbers together, and all the variables

-7x(3x+11)-(-6(-3x+5))=0

We multiply parentheses

-21x^2-77x-(-6(-3x+5))=0


We calculate terms in parentheses: -(-6(-3x+5)), so:

-6(-3x+5)

We multiply parentheses

18x-30

Back to the equation:

-(18x-30)


We get rid of parentheses

-21x^2-77x-18x+30=0

We add all the numbers together, and all the variables

-21x^2-95x+30=0

a = -21; b = -95; c = +30;
Δ = b2-4ac
Δ = -952-4·(-21)·30
Δ = 11545
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{-(-95)-\sqrt{11545}}{2*-21}=\frac{95-\sqrt{11545}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+\sqrt{11545}}{2*-21}=\frac{95+\sqrt{11545}}{-42}
$