(x+5)*3=x(5x-17)

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

(x+5)*3=x(5x-17)

We move all terms to the left:

(x+5)*3-(x(5x-17))=0

We multiply parentheses

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


We calculate terms in parentheses: -(x(5x-17)), so:

x(5x-17)

We multiply parentheses

5x^2-17x

Back to the equation:

-(5x^2-17x)


We get rid of parentheses

-5x^2+3x+17x+15=0

We add all the numbers together, and all the variables

-5x^2+20x+15=0

a = -5; b = 20; c = +15;
Δ = b2-4ac
Δ = 202-4·(-5)·15
Δ = 700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-10\sqrt{7}}{2*-5}=\frac{-20-10\sqrt{7}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+10\sqrt{7}}{2*-5}=\frac{-20+10\sqrt{7}}{-10}
$