7x^2=112+42x

Solution for 7x^2=112+42x equation:

7x^2=112+42x

We move all terms to the left:

7x^2-(112+42x)=0

We add all the numbers together, and all the variables

7x^2-(42x+112)=0

We get rid of parentheses

7x^2-42x-112=0

a = 7; b = -42; c = -112;
Δ = b2-4ac
Δ = -422-4·7·(-112)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-70}{2*7}=\frac{-28}{14}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+70}{2*7}=\frac{112}{14}
=8
$