4x^2+16x-23=10

Solution for 4x^2+16x-23=10 equation:

4x^2+16x-23=10

We move all terms to the left:

4x^2+16x-23-(10)=0

We add all the numbers together, and all the variables

4x^2+16x-33=0

a = 4; b = 16; c = -33;
Δ = b2-4ac
Δ = 162-4·4·(-33)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-28}{2*4}=\frac{-44}{8}
=-5+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+28}{2*4}=\frac{12}{8}
=1+1/2
$