5(x+6)=4x(x+7)

Solution for 5(x+6)=4x(x+7) equation:

5(x+6)=4x(x+7)

We move all terms to the left:

5(x+6)-(4x(x+7))=0

We multiply parentheses

5x-(4x(x+7))+30=0


We calculate terms in parentheses: -(4x(x+7)), so:

4x(x+7)

We multiply parentheses

4x^2+28x

Back to the equation:

-(4x^2+28x)


We get rid of parentheses

-4x^2+5x-28x+30=0

We add all the numbers together, and all the variables

-4x^2-23x+30=0

a = -4; b = -23; c = +30;
Δ = b2-4ac
Δ = -232-4·(-4)·30
Δ = 1009
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{-(-23)-\sqrt{1009}}{2*-4}=\frac{23-\sqrt{1009}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1009}}{2*-4}=\frac{23+\sqrt{1009}}{-8}
$