5(x+15)=x(x+7)

Solution for 5(x+15)=x(x+7) equation:

5(x+15)=x(x+7)

We move all terms to the left:

5(x+15)-(x(x+7))=0

We multiply parentheses

5x-(x(x+7))+75=0


We calculate terms in parentheses: -(x(x+7)), so:

x(x+7)

We multiply parentheses

x^2+7x

Back to the equation:

-(x^2+7x)


We get rid of parentheses

-x^2+5x-7x+75=0

We add all the numbers together, and all the variables

-1x^2-2x+75=0

a = -1; b = -2; c = +75;
Δ = b2-4ac
Δ = -22-4·(-1)·75
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{19}}{2*-1}=\frac{2-4\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{19}}{2*-1}=\frac{2+4\sqrt{19}}{-2}
$