Secondary Math Blogaroony

Firstly, the question should read, "find a quadratic equation...." as there are many....

(a) 

$(x-4)(x- -7)=0$

$x^2-4x+7x-28=0$

$x^2+3x-28=0$

(b) 

$(x-5-\sqrt{7})(x-5+\sqrt{7})=0$
$((x-5)-\sqrt{7})((x-5)+\sqrt{7})=0$

Thin difference of two squares.
$(x-5)^2-\sqrt{7}^2=0\\$
$(x-5)^2-7=0\\$
$x^2-10x+25 -7=0\\$
$x^2-10x+18=0$