2x(x+10)=5x-18

Solution for 2x(x+10)=5x-18 equation:

2x(x+10)=5x-18

We move all terms to the left:

2x(x+10)-(5x-18)=0

We multiply parentheses

2x^2+20x-(5x-18)=0

We get rid of parentheses

2x^2+20x-5x+18=0

We add all the numbers together, and all the variables

2x^2+15x+18=0

a = 2; b = 15; c = +18;
Δ = b2-4ac
Δ = 152-4·2·18
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-9}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+9}{2*2}=\frac{-6}{4}
=-1+1/2
$