x-10=3x(90+x)

Solution for x-10=3x(90+x) equation:

x-10=3x(90+x)

We move all terms to the left:

x-10-(3x(90+x))=0

We add all the numbers together, and all the variables

x-(3x(x+90))-10=0


We calculate terms in parentheses: -(3x(x+90)), so:

3x(x+90)

We multiply parentheses

3x^2+270x

Back to the equation:

-(3x^2+270x)


We get rid of parentheses

-3x^2+x-270x-10=0

We add all the numbers together, and all the variables

-3x^2-269x-10=0

a = -3; b = -269; c = -10;
Δ = b2-4ac
Δ = -2692-4·(-3)·(-10)
Δ = 72241
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{-(-269)-\sqrt{72241}}{2*-3}=\frac{269-\sqrt{72241}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-269)+\sqrt{72241}}{2*-3}=\frac{269+\sqrt{72241}}{-6}
$