12x^2=10-7x

Solution for 12x^2=10-7x equation:

12x^2=10-7x

We move all terms to the left:

12x^2-(10-7x)=0

We add all the numbers together, and all the variables

12x^2-(-7x+10)=0

We get rid of parentheses

12x^2+7x-10=0

a = 12; b = 7; c = -10;
Δ = b2-4ac
Δ = 72-4·12·(-10)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*12}=\frac{-30}{24}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*12}=\frac{16}{24}
=2/3
$