4x^2-42x=7x-12

Solution for 4x^2-42x=7x-12 equation:

4x^2-42x=7x-12

We move all terms to the left:

4x^2-42x-(7x-12)=0

We get rid of parentheses

4x^2-42x-7x+12=0

We add all the numbers together, and all the variables

4x^2-49x+12=0

a = 4; b = -49; c = +12;
Δ = b2-4ac
Δ = -492-4·4·12
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-47}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+47}{2*4}=\frac{96}{8}
=12
$