-17x+15=-3x(x-5)-14x

Solution for -17x+15=-3x(x-5)-14x equation:

-17x+15=-3x(x-5)-14x

We move all terms to the left:

-17x+15-(-3x(x-5)-14x)=0


We calculate terms in parentheses: -(-3x(x-5)-14x), so:

-3x(x-5)-14x

We add all the numbers together, and all the variables

-14x-3x(x-5)

We multiply parentheses

-3x^2-14x+15x

We add all the numbers together, and all the variables

-3x^2+x

Back to the equation:

-(-3x^2+x)


We get rid of parentheses

3x^2-x-17x+15=0

We add all the numbers together, and all the variables

3x^2-18x+15=0

a = 3; b = -18; c = +15;
Δ = b2-4ac
Δ = -182-4·3·15
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*3}=\frac{6}{6}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*3}=\frac{30}{6}
=5
$