5a^2=17a-10

Solution for 5a^2=17a-10 equation:

5a^2=17a-10

We move all terms to the left:

5a^2-(17a-10)=0

We get rid of parentheses

5a^2-17a+10=0

a = 5; b = -17; c = +10;
Δ = b2-4ac
Δ = -172-4·5·10
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-\sqrt{89}}{2*5}=\frac{17-\sqrt{89}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{89}}{2*5}=\frac{17+\sqrt{89}}{10}
$