12x^2+5x+10=17x^2+10

Solution for 12x^2+5x+10=17x^2+10 equation:

12x^2+5x+10=17x^2+10

We move all terms to the left:

12x^2+5x+10-(17x^2+10)=0

We get rid of parentheses

12x^2-17x^2+5x-10+10=0

We add all the numbers together, and all the variables

-5x^2+5x=0

a = -5; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-5)·0
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{-(5)-5}{2*-5}=\frac{-10}{-10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-5}=\frac{0}{-10}
=0
$