-5a+15/2a-25=53.2+21.8

Solution for -5a+15/2a-25=53.2+21.8 equation:

-5a+15/2a-25=53.2+21.8

We move all terms to the left:

-5a+15/2a-25-(53.2+21.8)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

-5a+15/2a-25-75=0

We add all the numbers together, and all the variables

-5a+15/2a-100=0

We multiply all the terms by the denominator


-5a*2a-100*2a+15=0

Wy multiply elements

-10a^2-200a+15=0

a = -10; b = -200; c = +15;
Δ = b2-4ac
Δ = -2002-4·(-10)·15
Δ = 40600
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:

$\sqrt{\Delta}=\sqrt{40600}=\sqrt{100*406}=\sqrt{100}*\sqrt{406}=10\sqrt{406}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-10\sqrt{406}}{2*-10}=\frac{200-10\sqrt{406}}{-20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+10\sqrt{406}}{2*-10}=\frac{200+10\sqrt{406}}{-20}
$