15x^2-29x-14=x(5x+2)

Solution for 15x^2-29x-14=x(5x+2) equation:

15x^2-29x-14=x(5x+2)

We move all terms to the left:

15x^2-29x-14-(x(5x+2))=0


We calculate terms in parentheses: -(x(5x+2)), so:

x(5x+2)

We multiply parentheses

5x^2+2x

Back to the equation:

-(5x^2+2x)


We get rid of parentheses

15x^2-5x^2-29x-2x-14=0

We add all the numbers together, and all the variables

10x^2-31x-14=0

a = 10; b = -31; c = -14;
Δ = b2-4ac
Δ = -312-4·10·(-14)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-39}{2*10}=\frac{-8}{20}
=-2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+39}{2*10}=\frac{70}{20}
=3+1/2
$