(2a)(a-5)=75

Solution for (2a)(a-5)=75 equation:

(2a)(a-5)=75

We move all terms to the left:

(2a)(a-5)-(75)=0

We multiply parentheses

2a^2-10a-75=0

a = 2; b = -10; c = -75;
Δ = b2-4ac
Δ = -102-4·2·(-75)
Δ = 700
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{7}}{2*2}=\frac{10-10\sqrt{7}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{7}}{2*2}=\frac{10+10\sqrt{7}}{4}
$