3x2-15x=4(x+2x2)-13

Solution for 3x2-15x=4(x+2x2)-13 equation:

3x^2-15x=4(x+2x^2)-13

We move all terms to the left:

3x^2-15x-(4(x+2x^2)-13)=0


We calculate terms in parentheses: -(4(x+2x^2)-13), so:

4(x+2x^2)-13

We multiply parentheses

8x^2+4x-13

Back to the equation:

-(8x^2+4x-13)


We add all the numbers together, and all the variables

3x^2-15x-(8x^2+4x-13)=0

We get rid of parentheses

3x^2-8x^2-15x-4x+13=0

We add all the numbers together, and all the variables

-5x^2-19x+13=0

a = -5; b = -19; c = +13;
Δ = b2-4ac
Δ = -192-4·(-5)·13
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-3\sqrt{69}}{2*-5}=\frac{19-3\sqrt{69}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+3\sqrt{69}}{2*-5}=\frac{19+3\sqrt{69}}{-10}
$