32a^2=7a+6

Solution for 32a^2=7a+6 equation:

32a^2=7a+6

We move all terms to the left:

32a^2-(7a+6)=0

We get rid of parentheses

32a^2-7a-6=0

a = 32; b = -7; c = -6;
Δ = b2-4ac
Δ = -72-4·32·(-6)
Δ = 817
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{817}}{2*32}=\frac{7-\sqrt{817}}{64}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{817}}{2*32}=\frac{7+\sqrt{817}}{64}
$