-3x(3x-7)=-2(x+4)+1

Solution for -3x(3x-7)=-2(x+4)+1 equation:

-3x(3x-7)=-2(x+4)+1

We move all terms to the left:

-3x(3x-7)-(-2(x+4)+1)=0

We multiply parentheses

-9x^2+21x-(-2(x+4)+1)=0


We calculate terms in parentheses: -(-2(x+4)+1), so:

-2(x+4)+1

We multiply parentheses

-2x-8+1

We add all the numbers together, and all the variables

-2x-7

Back to the equation:

-(-2x-7)


We get rid of parentheses

-9x^2+21x+2x+7=0

We add all the numbers together, and all the variables

-9x^2+23x+7=0

a = -9; b = 23; c = +7;
Δ = b2-4ac
Δ = 232-4·(-9)·7
Δ = 781
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{-(23)-\sqrt{781}}{2*-9}=\frac{-23-\sqrt{781}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+\sqrt{781}}{2*-9}=\frac{-23+\sqrt{781}}{-18}
$