(3-2x)(4x-7)=-8x-21

Solution for (3-2x)(4x-7)=-8x-21 equation:

(3-2x)(4x-7)=-8x-21

We move all terms to the left:

(3-2x)(4x-7)-(-8x-21)=0

We add all the numbers together, and all the variables

(-2x+3)(4x-7)-(-8x-21)=0

We get rid of parentheses

(-2x+3)(4x-7)+8x+21=0

We multiply parentheses ..

(-8x^2+14x+12x-21)+8x+21=0

We get rid of parentheses

-8x^2+14x+12x+8x-21+21=0

We add all the numbers together, and all the variables

-8x^2+34x=0

a = -8; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·(-8)·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*-8}=\frac{-68}{-16}
=4+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*-8}=\frac{0}{-16}
=0
$