10x^2-25x=-4x^2+6

Solution for 10x^2-25x=-4x^2+6 equation:

10x^2-25x=-4x^2+6

We move all terms to the left:

10x^2-25x-(-4x^2+6)=0

We get rid of parentheses

10x^2+4x^2-25x-6=0

We add all the numbers together, and all the variables

14x^2-25x-6=0

a = 14; b = -25; c = -6;
Δ = b2-4ac
Δ = -252-4·14·(-6)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-31}{2*14}=\frac{-6}{28}
=-3/14
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+31}{2*14}=\frac{56}{28}
=2
$