6-4x2=-7x-5

Solution for 6-4x2=-7x-5 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+7x+11=0

a = -4; b = 7; c = +11;
Δ = b2-4ac
Δ = 72-4·(-4)·11
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-15}{2*-4}=\frac{-22}{-8}
=2+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+15}{2*-4}=\frac{8}{-8}
=-1
$