(4x-5)2=14x2-47x+34

Solution for (4x-5)2=14x2-47x+34 equation:

(4x-5)2=14x^2-47x+34

We move all terms to the left:

(4x-5)2-(14x^2-47x+34)=0

We multiply parentheses

8x-(14x^2-47x+34)-10=0

We get rid of parentheses

-14x^2+8x+47x-34-10=0

We add all the numbers together, and all the variables

-14x^2+55x-44=0

a = -14; b = 55; c = -44;
Δ = b2-4ac
Δ = 552-4·(-14)·(-44)
Δ = 561
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{-(55)-\sqrt{561}}{2*-14}=\frac{-55-\sqrt{561}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{561}}{2*-14}=\frac{-55+\sqrt{561}}{-28}
$