X(5x+10)=10x+405

Solution for X(5x+10)=10x+405 equation:

X(5X+10)=10X+405

We move all terms to the left:

X(5X+10)-(10X+405)=0

We multiply parentheses

5X^2+10X-(10X+405)=0

We get rid of parentheses

5X^2+10X-10X-405=0

We add all the numbers together, and all the variables

5X^2-405=0

a = 5; b = 0; c = -405;
Δ = b2-4ac
Δ = 02-4·5·(-405)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90}{2*5}=\frac{-90}{10}
=-9
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90}{2*5}=\frac{90}{10}
=9
$