7x-16=x^2-10x+14

Solution for 7x-16=x^2-10x+14 equation:

7x-16=x^2-10x+14

We move all terms to the left:

7x-16-(x^2-10x+14)=0

We get rid of parentheses

-x^2+7x+10x-14-16=0

We add all the numbers together, and all the variables

-1x^2+17x-30=0

a = -1; b = 17; c = -30;
Δ = b2-4ac
Δ = 172-4·(-1)·(-30)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-13}{2*-1}=\frac{-30}{-2}
=+15
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+13}{2*-1}=\frac{-4}{-2}
=+2
$