4x2=12x+7

Solution for 4x2=12x+7 equation:

4x^2=12x+7

We move all terms to the left:

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

We get rid of parentheses

4x^2-12x-7=0

a = 4; b = -12; c = -7;
Δ = b2-4ac
Δ = -122-4·4·(-7)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16}{2*4}=\frac{28}{8}
=3+1/2
$