5a(8-5a)=4a-10

Solution for 5a(8-5a)=4a-10 equation:

5a(8-5a)=4a-10

We move all terms to the left:

5a(8-5a)-(4a-10)=0

We add all the numbers together, and all the variables

5a(-5a+8)-(4a-10)=0

We multiply parentheses

-25a^2+40a-(4a-10)=0

We get rid of parentheses

-25a^2+40a-4a+10=0

We add all the numbers together, and all the variables

-25a^2+36a+10=0

a = -25; b = 36; c = +10;
Δ = b2-4ac
Δ = 362-4·(-25)·10
Δ = 2296
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:

$\sqrt{\Delta}=\sqrt{2296}=\sqrt{4*574}=\sqrt{4}*\sqrt{574}=2\sqrt{574}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{574}}{2*-25}=\frac{-36-2\sqrt{574}}{-50}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{574}}{2*-25}=\frac{-36+2\sqrt{574}}{-50}
$