5x^2+12-4=30x-13

Solution for 5x^2+12-4=30x-13 equation:

5x^2+12-4=30x-13

We move all terms to the left:

5x^2+12-4-(30x-13)=0

We add all the numbers together, and all the variables

5x^2-(30x-13)+8=0

We get rid of parentheses

5x^2-30x+13+8=0

We add all the numbers together, and all the variables

5x^2-30x+21=0

a = 5; b = -30; c = +21;
Δ = b2-4ac
Δ = -302-4·5·21
Δ = 480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{30}}{2*5}=\frac{30-4\sqrt{30}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{30}}{2*5}=\frac{30+4\sqrt{30}}{10}
$