4a^2-2a=25-17a

Solution for 4a^2-2a=25-17a equation:

4a^2-2a=25-17a

We move all terms to the left:

4a^2-2a-(25-17a)=0

We add all the numbers together, and all the variables

4a^2-2a-(-17a+25)=0

We get rid of parentheses

4a^2-2a+17a-25=0

We add all the numbers together, and all the variables

4a^2+15a-25=0

a = 4; b = 15; c = -25;
Δ = b2-4ac
Δ = 152-4·4·(-25)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-25}{2*4}=\frac{-40}{8}
=-5
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+25}{2*4}=\frac{10}{8}
=1+1/4
$