E=(5x+8)(2x-7)

Solution for E=(5x+8)(2x-7) equation:

=(5E+8)(2E-7)

We move all terms to the left:

-((5E+8)(2E-7))=0

We multiply parentheses ..

-((+10E^2-35E+16E-56))=0


We calculate terms in parentheses: -((+10E^2-35E+16E-56)), so:

(+10E^2-35E+16E-56)

We get rid of parentheses

10E^2-35E+16E-56

We add all the numbers together, and all the variables

10E^2-19E-56

Back to the equation:

-(10E^2-19E-56)


We get rid of parentheses

-10E^2+19E+56=0

a = -10; b = 19; c = +56;
Δ = b2-4ac
Δ = 192-4·(-10)·56
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$E_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-51}{2*-10}=\frac{-70}{-20}
=3+1/2
$
$E_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+51}{2*-10}=\frac{32}{-20}
=-1+3/5
$