7x2=5x+2

Solution for 7x2=5x+2 equation:

7x^2=5x+2

We move all terms to the left:

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

We get rid of parentheses

7x^2-5x-2=0

a = 7; b = -5; c = -2;
Δ = b2-4ac
Δ = -52-4·7·(-2)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*7}=\frac{-4}{14}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*7}=\frac{14}{14}
=1
$