10y2+7y=12

Solution for 10y2+7y=12 equation:

10y^2+7y=12

We move all terms to the left:

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

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

$\sqrt{\Delta}=\sqrt{529}=23$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-23}{2*10}=\frac{-30}{20}
=-1+1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+23}{2*10}=\frac{16}{20}
=4/5
$