-8x+14=x(4x-7)

Solution for -8x+14=x(4x-7) equation:

-8x+14=x(4x-7)

We move all terms to the left:

-8x+14-(x(4x-7))=0


We calculate terms in parentheses: -(x(4x-7)), so:

x(4x-7)

We multiply parentheses

4x^2-7x

Back to the equation:

-(4x^2-7x)


We get rid of parentheses

-4x^2-8x+7x+14=0

We add all the numbers together, and all the variables

-4x^2-1x+14=0

a = -4; b = -1; c = +14;
Δ = b2-4ac
Δ = -12-4·(-4)·14
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-15}{2*-4}=\frac{-14}{-8}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+15}{2*-4}=\frac{16}{-8}
=-2
$