(x+5)(2x-7)-(14-4x)(3-2x)=0

Solution for (x+5)(2x-7)-(14-4x)(3-2x)=0 equation:

(x+5)(2x-7)-(14-4x)(3-2x)=0

We add all the numbers together, and all the variables

(x+5)(2x-7)-(-4x+14)(-2x+3)=0

We multiply parentheses ..

(+2x^2-7x+10x-35)-(-4x+14)(-2x+3)=0

We get rid of parentheses

2x^2-7x+10x-(-4x+14)(-2x+3)-35=0

We multiply parentheses ..

2x^2-(+8x^2-12x-28x+42)-7x+10x-35=0

We add all the numbers together, and all the variables

2x^2-(+8x^2-12x-28x+42)+3x-35=0

We get rid of parentheses

2x^2-8x^2+12x+28x+3x-42-35=0

We add all the numbers together, and all the variables

-6x^2+43x-77=0

a = -6; b = 43; c = -77;
Δ = b2-4ac
Δ = 432-4·(-6)·(-77)
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(43)-1}{2*-6}=\frac{-44}{-12}
=3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43)+1}{2*-6}=\frac{-42}{-12}
=3+1/2
$