-5x^2+6x+7=-x^2+4x

Solution for -5x^2+6x+7=-x^2+4x equation:

-5x^2+6x+7=-x^2+4x

We move all terms to the left:

-5x^2+6x+7-(-x^2+4x)=0

We get rid of parentheses

-5x^2+x^2-4x+6x+7=0

We add all the numbers together, and all the variables

-4x^2+2x+7=0

a = -4; b = 2; c = +7;
Δ = b2-4ac
Δ = 22-4·(-4)·7
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{29}}{2*-4}=\frac{-2-2\sqrt{29}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{29}}{2*-4}=\frac{-2+2\sqrt{29}}{-8}
$