(8x+7)(14x-11)=(5x+18)(10x+13)

Solution for (8x+7)(14x-11)=(5x+18)(10x+13) equation:

(8x+7)(14x-11)=(5x+18)(10x+13)

We move all terms to the left:

(8x+7)(14x-11)-((5x+18)(10x+13))=0

We multiply parentheses ..

(+112x^2-88x+98x-77)-((5x+18)(10x+13))=0


We calculate terms in parentheses: -((5x+18)(10x+13)), so:

(5x+18)(10x+13)

We multiply parentheses ..

(+50x^2+65x+180x+234)

We get rid of parentheses

50x^2+65x+180x+234

We add all the numbers together, and all the variables

50x^2+245x+234

Back to the equation:

-(50x^2+245x+234)


We get rid of parentheses

112x^2-50x^2-88x+98x-245x-77-234=0

We add all the numbers together, and all the variables

62x^2-235x-311=0

a = 62; b = -235; c = -311;
Δ = b2-4ac
Δ = -2352-4·62·(-311)
Δ = 132353
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{-(-235)-\sqrt{132353}}{2*62}=\frac{235-\sqrt{132353}}{124}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-235)+\sqrt{132353}}{2*62}=\frac{235+\sqrt{132353}}{124}
$