75+3x=60+3x(2x-1)

Solution for 75+3x=60+3x(2x-1) equation:

75+3x=60+3x(2x-1)

We move all terms to the left:

75+3x-(60+3x(2x-1))=0


We calculate terms in parentheses: -(60+3x(2x-1)), so:

60+3x(2x-1)

determiningTheFunctionDomain
3x(2x-1)+60

We multiply parentheses

6x^2-3x+60

Back to the equation:

-(6x^2-3x+60)


We get rid of parentheses

-6x^2+3x+3x-60+75=0

We add all the numbers together, and all the variables

-6x^2+6x+15=0

a = -6; b = 6; c = +15;
Δ = b2-4ac
Δ = 62-4·(-6)·15
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{11}}{2*-6}=\frac{-6-6\sqrt{11}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{11}}{2*-6}=\frac{-6+6\sqrt{11}}{-12}
$