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^2-25x+18=0

a = 2; b = -25; c = +18;
Δ = b2-4ac
Δ = -252-4·2·18
Δ = 481
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{-(-25)-\sqrt{481}}{2*2}=\frac{25-\sqrt{481}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{481}}{2*2}=\frac{25+\sqrt{481}}{4}
$