7x+2=5x*x

Solution for 7x+2=5x*x equation:

7x+2=5x*x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

7x-5x*x+2=0

Wy multiply elements

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

a = -5; b = 7; c = +2;
Δ = b2-4ac
Δ = 72-4·(-5)·2
Δ = 89
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{-(7)-\sqrt{89}}{2*-5}=\frac{-7-\sqrt{89}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{89}}{2*-5}=\frac{-7+\sqrt{89}}{-10}
$