5x(x-3)+6=4x+3

Solution for 5x(x-3)+6=4x+3 equation:

5x(x-3)+6=4x+3

We move all terms to the left:

5x(x-3)+6-(4x+3)=0

We multiply parentheses

5x^2-15x-(4x+3)+6=0

We get rid of parentheses

5x^2-15x-4x-3+6=0

We add all the numbers together, and all the variables

5x^2-19x+3=0

a = 5; b = -19; c = +3;
Δ = b2-4ac
Δ = -192-4·5·3
Δ = 301
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{-(-19)-\sqrt{301}}{2*5}=\frac{19-\sqrt{301}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{301}}{2*5}=\frac{19+\sqrt{301}}{10}
$