(2x-3)(-x+7)+13=4(-14x2+3x)+x(-x+4)

Solution for (2x-3)(-x+7)+13=4(-14x2+3x)+x(-x+4) equation:

(2x-3)(-x+7)+13=4(-14x^2+3x)+x(-x+4)

We move all terms to the left:

(2x-3)(-x+7)+13-(4(-14x^2+3x)+x(-x+4))=0

We add all the numbers together, and all the variables

-(4(-14x^2+3x)+x(-1x+4))+(2x-3)(-1x+7)+13=0

We multiply parentheses ..

-(4(-14x^2+3x)+x(-1x+4))+(-2x^2+14x+3x-21)+13=0


We calculate terms in parentheses: -(4(-14x^2+3x)+x(-1x+4)), so:

4(-14x^2+3x)+x(-1x+4)

We multiply parentheses

-56x^2-1x^2+12x+4x

We add all the numbers together, and all the variables

-57x^2+16x

Back to the equation:

-(-57x^2+16x)


We get rid of parentheses

57x^2-2x^2-16x+14x+3x-21+13=0

We add all the numbers together, and all the variables

55x^2+x-8=0

a = 55; b = 1; c = -8;
Δ = b2-4ac
Δ = 12-4·55·(-8)
Δ = 1761
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{-(1)-\sqrt{1761}}{2*55}=\frac{-1-\sqrt{1761}}{110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1761}}{2*55}=\frac{-1+\sqrt{1761}}{110}
$