x(x+7.5)=2(x+7.5)

Solution for x(x+7.5)=2(x+7.5) equation:

x(x+7.5)=2(x+7.5)

We move all terms to the left:

x(x+7.5)-(2(x+7.5))=0

We multiply parentheses

x^2+7.5x-(2(x+7.5))=0


We calculate terms in parentheses: -(2(x+7.5)), so:

2(x+7.5)

We multiply parentheses

2x+15

Back to the equation:

-(2x+15)


We get rid of parentheses

x^2+7.5x-2x-15=0

We add all the numbers together, and all the variables

x^2+5.5x-15=0

a = 1; b = 5.5; c = -15;
Δ = b2-4ac
Δ = 5.52-4·1·(-15)
Δ = 90.25
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{-(5.5)-\sqrt{90.25}}{2*1}=\frac{-5.5-\sqrt{90.25}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5.5)+\sqrt{90.25}}{2*1}=\frac{-5.5+\sqrt{90.25}}{2}
$