4x(2x-5)=3x-14

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

4x(2x-5)=3x-14

We move all terms to the left:

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

We multiply parentheses

8x^2-20x-(3x-14)=0

We get rid of parentheses

8x^2-20x-3x+14=0

We add all the numbers together, and all the variables

8x^2-23x+14=0

a = 8; b = -23; c = +14;
Δ = b2-4ac
Δ = -232-4·8·14
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-9}{2*8}=\frac{14}{16}
=7/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+9}{2*8}=\frac{32}{16}
=2
$