7x^2=25x-12

Solution for 7x^2=25x-12 equation:

7x^2=25x-12

We move all terms to the left:

7x^2-(25x-12)=0

We get rid of parentheses

7x^2-25x+12=0

a = 7; b = -25; c = +12;
Δ = b2-4ac
Δ = -252-4·7·12
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-17}{2*7}=\frac{8}{14}
=4/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+17}{2*7}=\frac{42}{14}
=3
$