7.5x^2-15x=60

Solution for 7.5x^2-15x=60 equation:

7.5x^2-15x=60

We move all terms to the left:

7.5x^2-15x-(60)=0

a = 7.5; b = -15; c = -60;
Δ = b2-4ac
Δ = -152-4·7.5·(-60)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-45}{2*7.5}=\frac{-30}{15}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+45}{2*7.5}=\frac{60}{15}
=4
$