2x-7=5x^2-7

Solution for 2x-7=5x^2-7 equation:

2x-7=5x^2-7

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2+2x=0

a = -5; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-5)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-5}=\frac{-4}{-10}
=2/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-5}=\frac{0}{-10}
=0
$