90=x(3x+10)

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

90=x(3x+10)

We move all terms to the left:

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


We calculate terms in parentheses: -(x(3x+10)), so:

x(3x+10)

We multiply parentheses

3x^2+10x

Back to the equation:

-(3x^2+10x)


We get rid of parentheses

-3x^2-10x+90=0

a = -3; b = -10; c = +90;
Δ = b2-4ac
Δ = -102-4·(-3)·90
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{295}}{2*-3}=\frac{10-2\sqrt{295}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{295}}{2*-3}=\frac{10+2\sqrt{295}}{-6}
$