4x2-24x+-7=-3

Solution for 4x2-24x+-7=-3 equation:

4x^2-24x+-7=-3

We move all terms to the left:

4x^2-24x+-7-(-3)=0

We add all the numbers together, and all the variables

4x^2-24x-4=0

a = 4; b = -24; c = -4;
Δ = b2-4ac
Δ = -242-4·4·(-4)
Δ = 640
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:

$\sqrt{\Delta}=\sqrt{640}=\sqrt{64*10}=\sqrt{64}*\sqrt{10}=8\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{10}}{2*4}=\frac{24-8\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{10}}{2*4}=\frac{24+8\sqrt{10}}{8}
$