5x(x-6)+2=7x-8

Solution for 5x(x-6)+2=7x-8 equation:

5x(x-6)+2=7x-8

We move all terms to the left:

5x(x-6)+2-(7x-8)=0

We multiply parentheses

5x^2-30x-(7x-8)+2=0

We get rid of parentheses

5x^2-30x-7x+8+2=0

We add all the numbers together, and all the variables

5x^2-37x+10=0

a = 5; b = -37; c = +10;
Δ = b2-4ac
Δ = -372-4·5·10
Δ = 1169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{1169}}{2*5}=\frac{37-\sqrt{1169}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1169}}{2*5}=\frac{37+\sqrt{1169}}{10}
$