7a^2-14a=25

Solution for 7a^2-14a=25 equation:

7a^2-14a=25

We move all terms to the left:

7a^2-14a-(25)=0

a = 7; b = -14; c = -25;
Δ = b2-4ac
Δ = -142-4·7·(-25)
Δ = 896
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-8\sqrt{14}}{2*7}=\frac{14-8\sqrt{14}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+8\sqrt{14}}{2*7}=\frac{14+8\sqrt{14}}{14}
$