4x-3=3x(x-5)+2

Solution for 4x-3=3x(x-5)+2 equation:

4x-3=3x(x-5)+2

We move all terms to the left:

4x-3-(3x(x-5)+2)=0


We calculate terms in parentheses: -(3x(x-5)+2), so:

3x(x-5)+2

We multiply parentheses

3x^2-15x+2

Back to the equation:

-(3x^2-15x+2)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+19x-5=0

a = -3; b = 19; c = -5;
Δ = b2-4ac
Δ = 192-4·(-3)·(-5)
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*-3}=\frac{-19-\sqrt{301}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{301}}{2*-3}=\frac{-19+\sqrt{301}}{-6}
$