1.5x(x+7)=11.25

Solution for 1.5x(x+7)=11.25 equation:

1.5x(x+7)=11.25

We move all terms to the left:

1.5x(x+7)-(11.25)=0

We add all the numbers together, and all the variables

1.5x(x+7)-11.25=0

We multiply parentheses

x^2+7x-11.25=0

a = 1; b = 7; c = -11.25;
Δ = b2-4ac
Δ = 72-4·1·(-11.25)
Δ = 94
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{-(7)-\sqrt{94}}{2*1}=\frac{-7-\sqrt{94}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{94}}{2*1}=\frac{-7+\sqrt{94}}{2}
$