7m2+8m=3

Solution for 7m2+8m=3 equation:

7m^2+8m=3

We move all terms to the left:

7m^2+8m-(3)=0

a = 7; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·7·(-3)
Δ = 148
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{37}}{2*7}=\frac{-8-2\sqrt{37}}{14}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{37}}{2*7}=\frac{-8+2\sqrt{37}}{14}
$