5x(x-55)=2(3x-12)

Solution for 5x(x-55)=2(3x-12) equation:

5x(x-55)=2(3x-12)

We move all terms to the left:

5x(x-55)-(2(3x-12))=0

We multiply parentheses

5x^2-275x-(2(3x-12))=0


We calculate terms in parentheses: -(2(3x-12)), so:

2(3x-12)

We multiply parentheses

6x-24

Back to the equation:

-(6x-24)


We get rid of parentheses

5x^2-275x-6x+24=0

We add all the numbers together, and all the variables

5x^2-281x+24=0

a = 5; b = -281; c = +24;
Δ = b2-4ac
Δ = -2812-4·5·24
Δ = 78481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-281)-\sqrt{78481}}{2*5}=\frac{281-\sqrt{78481}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-281)+\sqrt{78481}}{2*5}=\frac{281+\sqrt{78481}}{10}
$