x(5x+3)=2x^2-2x+28

Solution for x(5x+3)=2x^2-2x+28 equation:

x(5x+3)=2x^2-2x+28

We move all terms to the left:

x(5x+3)-(2x^2-2x+28)=0

We multiply parentheses

5x^2+3x-(2x^2-2x+28)=0

We get rid of parentheses

5x^2-2x^2+3x+2x-28=0

We add all the numbers together, and all the variables

3x^2+5x-28=0

a = 3; b = 5; c = -28;
Δ = b2-4ac
Δ = 52-4·3·(-28)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-19}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+19}{2*3}=\frac{14}{6}
=2+1/3
$