7x+3=-16x^2+20x+6

Solution for 7x+3=-16x^2+20x+6 equation:

7x+3=-16x^2+20x+6

We move all terms to the left:

7x+3-(-16x^2+20x+6)=0

We get rid of parentheses

16x^2-20x+7x-6+3=0

We add all the numbers together, and all the variables

16x^2-13x-3=0

a = 16; b = -13; c = -3;
Δ = b2-4ac
Δ = -132-4·16·(-3)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-19}{2*16}=\frac{-6}{32}
=-3/16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*16}=\frac{32}{32}
=1
$