10x^2-23x+12=-15x^2+12x

Solution for 10x^2-23x+12=-15x^2+12x equation:

10x^2-23x+12=-15x^2+12x

We move all terms to the left:

10x^2-23x+12-(-15x^2+12x)=0

We get rid of parentheses

10x^2+15x^2-12x-23x+12=0

We add all the numbers together, and all the variables

25x^2-35x+12=0

a = 25; b = -35; c = +12;
Δ = b2-4ac
Δ = -352-4·25·12
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5}{2*25}=\frac{30}{50}
=3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5}{2*25}=\frac{40}{50}
=4/5
$