8x^2=12-10x

Solution for 8x^2=12-10x equation:

8x^2=12-10x

We move all terms to the left:

8x^2-(12-10x)=0

We add all the numbers together, and all the variables

8x^2-(-10x+12)=0

We get rid of parentheses

8x^2+10x-12=0

a = 8; b = 10; c = -12;
Δ = b2-4ac
Δ = 102-4·8·(-12)
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-22}{2*8}=\frac{-32}{16}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+22}{2*8}=\frac{12}{16}
=3/4
$