5x2=-7+12x

Solution for 5x2=-7+12x equation:

5x^2=-7+12x

We move all terms to the left:

5x^2-(-7+12x)=0

We add all the numbers together, and all the variables

5x^2-(12x-7)=0

We get rid of parentheses

5x^2-12x+7=0

a = 5; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·5·7
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2}{2*5}=\frac{10}{10}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2}{2*5}=\frac{14}{10}
=1+2/5
$