(x-5)(x+2)=4(3x-16)

Solution for (x-5)(x+2)=4(3x-16) equation:

(x-5)(x+2)=4(3x-16)

We move all terms to the left:

(x-5)(x+2)-(4(3x-16))=0

We multiply parentheses ..

(+x^2+2x-5x-10)-(4(3x-16))=0


We calculate terms in parentheses: -(4(3x-16)), so:

4(3x-16)

We multiply parentheses

12x-64

Back to the equation:

-(12x-64)


We get rid of parentheses

x^2+2x-5x-12x-10+64=0

We add all the numbers together, and all the variables

x^2-15x+54=0

a = 1; b = -15; c = +54;
Δ = b2-4ac
Δ = -152-4·1·54
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3}{2*1}=\frac{12}{2}
=6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3}{2*1}=\frac{18}{2}
=9
$