5a^2-7a=3

Solution for 5a^2-7a=3 equation:

5a^2-7a=3

We move all terms to the left:

5a^2-7a-(3)=0

a = 5; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·5·(-3)
Δ = 109
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{109}}{2*5}=\frac{7-\sqrt{109}}{10}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{109}}{2*5}=\frac{7+\sqrt{109}}{10}
$