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

Solution for 14x^2-8x=7x-4 equation:

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

We move all terms to the left:

14x^2-8x-(7x-4)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

14x^2-15x+4=0

a = 14; b = -15; c = +4;
Δ = b2-4ac
Δ = -152-4·14·4
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{-(-15)-1}{2*14}=\frac{14}{28}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+1}{2*14}=\frac{16}{28}
=4/7
$