-5x^2+2=7x

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

-5x^2+2=7x

We move all terms to the left:

-5x^2+2-(7x)=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}
$