5x^2=17X-12

Solution for 5x^2=17X-12 equation:

5x^2=17x-12

We move all terms to the left:

5x^2-(17x-12)=0

We get rid of parentheses

5x^2-17x+12=0

a = 5; b = -17; c = +12;
Δ = b2-4ac
Δ = -172-4·5·12
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7}{2*5}=\frac{24}{10}
=2+2/5
$