5x^2=34x-24

Solution for 5x^2=34x-24 equation:

5x^2=34x-24

We move all terms to the left:

5x^2-(34x-24)=0

We get rid of parentheses

5x^2-34x+24=0

a = 5; b = -34; c = +24;
Δ = b2-4ac
Δ = -342-4·5·24
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-34)-26}{2*5}=\frac{8}{10}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-34)+26}{2*5}=\frac{60}{10}
=6
$