7x2+3x=5

Solution for 7x2+3x=5 equation:

7x^2+3x=5

We move all terms to the left:

7x^2+3x-(5)=0

a = 7; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·7·(-5)
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{149}}{2*7}=\frac{-3-\sqrt{149}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{149}}{2*7}=\frac{-3+\sqrt{149}}{14}
$