7x+16=5x(x-3)

Solution for 7x+16=5x(x-3) equation:

7x+16=5x(x-3)

We move all terms to the left:

7x+16-(5x(x-3))=0


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

5x(x-3)

We multiply parentheses

5x^2-15x

Back to the equation:

-(5x^2-15x)


We get rid of parentheses

-5x^2+7x+15x+16=0

We add all the numbers together, and all the variables

-5x^2+22x+16=0

a = -5; b = 22; c = +16;
Δ = b2-4ac
Δ = 222-4·(-5)·16
Δ = 804
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:

$\sqrt{\Delta}=\sqrt{804}=\sqrt{4*201}=\sqrt{4}*\sqrt{201}=2\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{201}}{2*-5}=\frac{-22-2\sqrt{201}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{201}}{2*-5}=\frac{-22+2\sqrt{201}}{-10}
$