4x(x+8)=3x(x+26)

Solution for 4x(x+8)=3x(x+26) equation:

4x(x+8)=3x(x+26)

We move all terms to the left:

4x(x+8)-(3x(x+26))=0

We multiply parentheses

4x^2+32x-(3x(x+26))=0


We calculate terms in parentheses: -(3x(x+26)), so:

3x(x+26)

We multiply parentheses

3x^2+78x

Back to the equation:

-(3x^2+78x)


We get rid of parentheses

4x^2-3x^2+32x-78x=0

We add all the numbers together, and all the variables

x^2-46x=0

a = 1; b = -46; c = 0;
Δ = b2-4ac
Δ = -462-4·1·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-46}{2*1}=\frac{0}{2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+46}{2*1}=\frac{92}{2}
=46
$