X(7x+5)=2x^2-14x+4

Solution for X(7x+5)=2x^2-14x+4 equation:

X(7X+5)=2X^2-14X+4

We move all terms to the left:

X(7X+5)-(2X^2-14X+4)=0

We multiply parentheses

7X^2+5X-(2X^2-14X+4)=0

We get rid of parentheses

7X^2-2X^2+5X+14X-4=0

We add all the numbers together, and all the variables

5X^2+19X-4=0

a = 5; b = 19; c = -4;
Δ = b2-4ac
Δ = 192-4·5·(-4)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-21}{2*5}=\frac{-40}{10}
=-4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+21}{2*5}=\frac{2}{10}
=1/5
$